Chasseurs were born in 1473, and were very similar to German Jaegers mission and equipment wise. They were lightly armed with a Fusil, and fought as light infantry, they were often supporting Volteguiers in rangery.
As time passed, Chasseur cavalry, and line infantry regiments were made, eventually Guards Chasseur units started being formed.
In the modern world, the Chasseurs are used as lightly armed infantrymen, trained to fight in rugged terrain that doesn't favor armored or heavy infantry formations. They scout and secure untrustworthy terrain, just like Jagers in modern times.
Chasseurs are light infantry who are trusted with fighting in and clearing ground on untrusted or uneven terrain, for example: jungles, mountains, hills, urban areas. They are lightly armed, unlike regular French basic infantry, so they can easily maneuver on the uneven terrain, and scout ahead. Chasseurs have many similarities to the German "Jaegers" in the real world (Jager also means "hunter"), the same can be said about them in Napoleonic times, as both units specialized in skirmishing and rangery.
Chasseurs armed with the FAMAS are low in availability (20 units), but they are very cheap, are armed very well, the FAMAS they use has the most fire rate for an assault rifle in the entire game even though the calibre is weak, they also have very good LAW anti tank weapons, they also have very fast transports, like the VAB. Like other French units, you should focus on ambushing with these units, and meeting infantry threats quickly using the incredibly fast transports. There are also regular Chasseurs armed with the MAS 49/56 semi-automatic battle rifle, costing only 5 points less while having significantly less ammunition, worse accuracy and low rate of fire.