Betancourt travels to Paris at the end of March 1784 in company of Alonso de Nava to study “geometry and underground architecture”, denomination of the time for mining. He studies at l’École des Ponts et Chaussés, the French School of Roads, where he meets the engineers Jean Rodolphe Perronet and Gaspard Riche de Prony as well as Gaspard Monge, founder of Descriptive Geometry. He studies the theme of the purification of stone coal at the furnaces of the Parisian Jardin des Plantes, where they extracted the bitumen from the coal.

Paris is, at that moment, the capital of the world referring to scientific and technological studies, besides being the capital of political modernity. Five years after his arrival, in 1789, the French revolution takes place. In the middle of these political changes, that mean the fall of the Ancien Régime and the beginning of the Contemporary History of Europe, Betancourt remains in France, until 1791.

In July 1785 his brother José de Betancourt y Castro arrives in Paris, both collaborate for three years in the search for machines and are in charge of the group of Spanish scholars that Agustín coordinates. The scholars, and the Betancourt brothers themselves, made several inspection trips to different regions and places of France.

Interval in Madrid (August 17^th, 1785 - September 10^th, 1785)

He discusses with the Conde de Floridablanca about the possibility of creating a School of Bridges and Roads in Spain that would take the French one as a model, and also about the reorientation of his studies on hydraulics and mechanics. He probably collaborates with the chemist Louis Proust, who was then working in Spain, on a method to whiten silk, and writes a lost memoir titled Memoria sobre el mejor modo de blanquear la seda.

He presents in Paris his Memoria sobre la purificación del carbón de piedra y modo de aprovechar las materias que contiene dedicated to Carlos III, describing the furnaces of Ireland and those of the Jardin des Plantes, and proposing a new model of closed furnace to make coke.

At the beginning of 1786, Betancourt officially dedicates himself to hydraulics and mechanics, gathering plans of useful machines and sending books about this theme to Spain. He begins to organize the preparation of the scholars that were assigned to him, that in the first moment were Tomás de Verí y Togorés, Juan de la Fuente y Antonio Álvarez (from October 1786).

This could be the date of a lost memoir, supposedly identical to the one mentioned above, titled Memoria sobre el método de construir y usar los hornos para extraer el betún que tiene el carbón de piedra, quedando éste purificado al mismo tiempo which was sent to the Real Sociedad Económica de Amigos del País de Asturias, society where Betancourt was named a worthy honorary member (the furnaces, however, didn’t give a good result, due to some building defect).

Betancourt designed a loom to make wide ribbons of satin and taffeta (the model was later incorporated to the Gabinete de Máquinas).

In 1787 he strengthens his friendship with the Swiss French watchmaker Abraham Louis Breguet, with whom he will be commercially associated selling watches since then. This same year the creation of the Real Gabinete de Máquinas is made official of which Betancourt will be named director in December although he will not take possession of the post until April 1792. During that year Betancourt and his collaborators dedicated themselves in Paris to look for all kinds of machines, artefacts and constructions, many of them for hydraulics or for public works but also of metallurgy destined to the textile industry, to be incorporated to the Real Gabinete.

In 1788 our engineer invents a machine to make ribbons as an ornament for ladies. In March of this year he makes an excursion with his brother José to Brittany to study the ports of the region [See manuscript notes of this trip: Letter 3].

A letter of his brother José is conserved written from Madrid to his father where he tells something about the special missions for which he was sent to France and England as right hand man of the Conde de Floridablanca. In it he talks about secrets of State and of the purest industrial spying to obtain plans of machines -in this case warships- and of the money paid for these services. [See Letter from José de Betancourt to his father October 28th, 1788: Letter 6].

First month long trip of the Canarian engineer to England. He goes to Birmingham interested in steam engines. There Watt and his partner Boulton talk to Betancourt about them and their advantages in general but they refused to show him any. Back in London he is able to see one functioning near Blackfriars Bridge and although it was partially covered up by a partition he can observe the double run of the piston through the cylinder. Although he does not see the machine in its totality this did not prevent, on returning to France, that he was able to build a double effect steam engine. In this way he is the introducer of the steam engine to the European continent: a machine different to the English one as he had to rebuild parts of it that he had not been able to see in England.

It is possible that Betancourt could also find out (or copy) the working order of a secret English loom that he built on his return to France, and that figured later on in the Gabinete de Máquinas.

He begins his studies on water vapour and to work on the steam engine. While Betancourt is in England Juan López de Peñalver asks to be moved to Paris to work with him.

In January 1789 he tells his family about the invention of an eolian machine to drain water from swampy land (it will be in the collection of the Gabinete). In this same letter he talks about the exact drawings of machines that he did in England, as well as his growing influence upon the Minister of State, Floridablanca, and of how he has put him in charge of the scholars. [See Letter from Betancourt to his parents January 10^th, 1789: Letter 9].

He also writes to his parents in March saying he is busy with a collection of physical instruments –for the Malaspina expedition? - And that he is working on “the collection of hydraulic models” with four cabinetmakers, seven locksmiths, and three draughtsmen. In the letter he is very proud of creating “the best Gabinete de Máquinas that there will be in Europe”. [See Letter from Betancourt to his parents March 6^th, 1789: Letter 11].

The Spanish ambassador Fernán Núñez sends the Índice de los Modelos y Memorias de don Agustín de Betancourt to Madrid, which is an advance of the Catalogue of the Gabinete.

The Chevalier de Borda and Gaspard Monge, commissioned by the French Academy of Sciences, inform favourably, in February 1790, on the Memoria de una máquina de vapor de doble efecto. In March of the previous year, Betancourt had already agreed with the Périer Brothers to the construction of a flour factory with mills activated by a double effect steam engine, that in November 1790 works successfully at the Island of Swans; it is the first steam engine that works outside England, on the continent. In a letter to his brother José in March 1789 he told him the following: “My model of fire pump has experimented terrible mutations with my trip to London. Of the pieces that were made, hardly a quarter of them were used and although I have left the same steam cylinder, it will have double strength. Messrs Périer have seen the plans that I have made and they are so happy with them that they are going to make a big one with all the innovations that I have practised.” [See Letter from Betancourt to his brother José March 6^th, 1789: Letter 12].

In September of the same year, Borda, Monge and Brisson give their approval to the Mémoire sur la force expansive de la vapeur de l’eau, that will be published at the end of the year; it is one of the Canarian engineer’s works with the biggest theoretical charge which, in its study of the relationship between pressure and temperature, advances future thermodynamic laws.

In 1791 Betancourt finishes one of his last works in Paris: his Descripción del Real Establecimiento de Yndrid donde se funden y barrenan los cañones de hierro para la Marina Real de Francia. In February of this year they receive the order to move back to Spain in view of the way the events are going in Revolutionary France. Between March and May they pack up all the material of what will later become the Real Gabinete de Máquinas, from July on, starting with the plans, the collection of machines begins to arrive in Madrid. On July 20^th, Betancourt and Peñalver subscribe the Memoria sobre los medios para facilitar el comercio interior, where they include multiple considerations about the construction and improvement of the roads and canals of Spain and the need to establish a school to form future engineers to build them; the proposal of a future Escuela de Caminos y Canales had been made months before to Floridablanca.

It is in the last two years in Paris, when Betancourt contacts the Mexican José María de Lanz with whom he later collaborates at the Escuela de Caminos and with whom he will write his book on machines. Also during these years Betancourt marries the English lady Anna Jourdain –whom he marries three times.