The artillery was in charge of small arms production. The Revolutionary governments had fouled up weapons production and it wasn't until 1796-1799 that the Directory reinstated the artillery as the overall supervisor of weapons production.
The last Royal Army model of musket was that of 1777. Napoleon ordered a commission of artillery officers 'to establish the necessary new models of individual weapons. The 'new' musket of the 'System of the Year Nine (1800-1801) was a simplified version of the model 1777. More improvements in musket design were made in the 'Year Thirteen' (1804-1805).
In 1804 the army took over production of individual weapons for the Navy and in 1803 there were some 800,000 muskets and carbines either with the troops or in the arsenals. These were classed in three groups-the first were regulation models which were issued to regular units. The second group of old and discontinued models were issued to the National Guard and irregular units. The third class were 'everything else,' which included captured weapons.
An excellent reference for the French models of muskets and their production is Engineering the Revolution by Ken Alder.
The French regulation musket, older models as well as the model 1777, were sent to North America during the War of the Revolution. They were known by the US troops as the Charleville because that was one of the armories that produced the excellent French muskets. These became the issue musket for the Continental Army and was believed to be superior to the British Brown Bess. The excellent US Springfield musket model 1795 was copied from the French Charleville.
Another excellent reference for the French musket models that were sent to the Continental Army is The Book of the Continental Soldier by Harold Peterson.
The official models of French muskets were those of 1763, 1766, 1768 (possible), 1770-1771, 1773, 1774, and 1777. Probably few if any of the model 1777 were sent to the new United States as they were being issued to the French army as they were produced. There were some differences between models, but all were of a general pattern. All were excellent muskets and all were known by the Continental Army as Charlevilles no matter where they were manufactured.