Upvote:5
I would definitely apply for a multiple entry visa from the French embassy, which will be cheaper and less hassle. If this is your first Schengen visa, you will need to present documentation for both trips to prove that you need multiple entries, since otherwise they will only give you a single entry. Having a business/educational need to travel with invitation letters from professors etc will also increase the odds of success.
If you are only granted single entry, then it's back to plan B: apply for a second single entry from Spain.