There's a lot of overlap between AF Flying Blue and DL SkyMiles. Those two airlines are in the same alliance, so you can credit flights on either airline to either program. Each also has a few non-alliance partners that it doesn't share with the other, but those are minor. You might as well join both for this reason, since joining is free, but plan to credit most of your AF/DL flights to the same program, whichever it is. That will also help you reach elite status faster, with many attendant benefits.

I don't know enough about FB to recommend one over the other, but you can look at earning potential at the fare classes you expect to fly in, mileage requirements for awards (keeping in mind that awards at the lowest level can be hard to find on DL, unless you book very early or accept flight times that nobody likes), requirements for elite status, and the fact that some benefits (such as free upgrades) are reserved for an airline's own elite members regardless of what status they have with alliance partners.