French Bombardiers are different from what one would expect.

Bombardiers unifor15

The French, much like the British in the late 17th century, raise regiments for sea duty and eventually transferred them to the Army establishment. The Bombardiers, however, were raised in small detachments in coastal fortresses to man the mortars both on board ship and in the fortresses. Their uniforms remained broadly the same throughout this period, red coats faced with blue. As can be seen at Figure 9, without the coat the appearance is very different--all blue. The one figure with a blue coat is likely a Canonnier--they wore blue.

uniformology01bombardie

This print shows alternate grenadier caps. Some companies seem to have worn grenadier caps and others tricornes.

1750 marine  bombardiers de la marine small

Here's another print, from 1750.

Don't know that any of these troops served in North America or the Caribbean--but who cares? They're pretty cool and very different from the blue and white of the rest of the French troops.

I don't have the key to the Eugene Lelieprve print at the top but I'll update the post if I find it.