If you want to surf, take a pure surf SUP shape. Anything goes for fitness.
"flat water" shapes are good only when cruising with friends, so they do not have to wait for you.
But for fitness alone, I was using my 7'10" (I am 100kg) for fitness sessions around the "Ile de Lerins". It took me 2 hours instead of 1h15 with a 12'6", but it was a very good training for surfing.
And paddling on a small SUP is harder than a long SUP, so it is a better exercise, and you learn more to control the row.
So just focus on the wave performance, forget the flat water, unless you want to race or do cruises to far away places (islands...)
This said, as you are in France, I suggest you check the Gong line (and other French brands). They offer really innovative shapes in quality construction, designed for French waves (with a fast rocker), at a nice price (you can get a quiver for the price of other boards). Try to find an ambassador near you to look at them or even try them:
www.gong-galaxy.com/forum/viewtopic.php?f=31&t=2225 or
www.gongsup.com/Ambassadors.html?lang=frShops do not like them, so you will hear bad things on them from shop vendors, try to get the other side of the story with actual Gong owners.
If you are near Cannes, I can show them to you. Disclaimer: I am a Gong ambassador :-)