What is the difference between Paris ham and French ham?
Jambon de Paris (Paris Ham) is a slow cooked ham. The slow cooking means it retains a large percentage of its moisture and absorbs the flavours of the ingredients with which it is cooked.

Jambon de Bayonne is a dry cured or smoked ham that may or may not be further cured in red wine and given its name from the region in which it originates.

Both are sometimes identified as French Jambon ham. French-style ham would probably indicate the use of one or both methods to produce the final result. But as Elendilthetall mentioned it is just marketing speak for an imitation.