I have Lynn’s and Griffith’s books on the French Revolutionary armies, but those don’t discuss uniforms. Would soldiers in the same unit wear a mix of helmets and bicorns or would they tend to wear identical headgear within the same unit?
I think soldiers in the same unit would generally wear the same headgear. According to Philip Haythornthwaite’s Uniforms of the French Revolutionary Wars the crested Tarleton-style helmet replaced the bicorn hat in 1791 but not all units received it. The new headgear was unpopular and Haythornthwaite relates the example of the 46th regiment which didn’t receive their helmets until 1793 and only wore them until 1796 “by which time they were so smelly that in a mass demonstration the whole regiment threw them into the river at Strasbourg.” They then apparently paid five francs per man to buy themselves hats. However, he also notes that the 9th Demi-Brigade kept their helmets at least until 1798.
The grenadier companies would have worn grenadier caps (which were reintroduced in 1789) whether the rest of the regiment were wearing hats or helmets.