If the flights are operated by Delta, you can simply add the flights to your skymiles account on Delta's website/app using the ticket number or confirmation code in My Trips. (You'll also have to do this to pick seats if your flights are operated by Delta.)

If they're operated by anyone else this truct won't work. I recently had an AF reservation, ATL-CDG on DL and CDG-ATL on AF. I made the mistake of adding my FlyingBlue number on AF's website, and couldn't change it at all. Thankfully, I did the Delta trick above and confirmed at check-in that my skymiles number was on my boarding pass, and everything credited correctly.

As a side note, you don't mention your flights or operating carrier. Though you are flying to Paris, I doubt you'll have any issues with this: As you're relatively new you all of this, make sure you explore this page and fully understand what flights are eligible for earning miles with Delta. Also, know that flights with flight numbers other than Delta's earn based on distance and a percentage of that based on your fare class. So V class on AF689 will earn 25% of the distance between ATL-CDG. Same on AF3595, even though that's actually DL84.

Hope this helps and welcome to FT!