Welcome to FT-AA!
At this late a date, I don't have much hope for your aspirations. I would snatch those relatively cheap (in today's pricing environment) $675 flights now, or begin to plan for one paid and one award seat - if you can find one available. Try TN JFK-CDG - I think you'd have the best luck there with AA miles, and iirc the flights have been less than full; one paid and one award seat might be available - moreso with a little date flexibility.