These are all based on factual events *here*.
The first "air force" (of a sort) *here* was created in 1794. It was composed of a few men who used gaz-filled Balloons (a recent innovation) to observe the ennemy troops. It proved to be such a tactical improvement that the french government funded a Balloonist School and 2 companies of "Aerostier" to men and maintain them. The director of the institution was Nicholas Conté (inventor amongst other things, of the lead pencil).
Unfortunatly, all the equipment were lost during the crossing of the mediteranean on its way to egypt. The general in charge, Napoleon, disbanded the unit around 1797. For all his strategic accumen, Napoleon was nefariously reticent when it came to using technological invention in war. He famously refused to consider firearm innovation that ended up being used decades later.
Conté apparently wanted to develop things such as dirigible ballons that could then bombard ennemy troops from above. With the closure of the school, this came to nothing and it is in 1852 that another inventor, Henri Giffar, manage to create a navigatable balloon.
- There*, the school remained open allowing continued reserach and other companies of aerostier being created. Although this doesn't mean jetplanes by the mid-19th century, it would have meant that the air industry would probably be a few decades in advance compared to *here*.