프랑스어는 한국어와 많이 달라요. = French is very different from Korean. 프랑스어는 한국어와 진짜 달라요.= French is 'different' from Korean for sure.(emphasis on different) I see no much difference between them.But 진짜 sounds more colloquial. I would say more people will use 프랑스어는 한국어와 매우 달라요. more often than ~많이(or 진짜) 달라요. 매우 is commonly used to make an emphasize on a adjective or a adverb.

진짜 is translated as "really", but it really means "for real". 가짜 is fake. Like 가짜 손톱 means fake (finger)nails. So by "really" it means in truth, for sure, etc. Just a slight difference in nuance in most cases.