I don't know if there is any transfer possible btwn terminals without leaving the secured area.
However, if you DO have to leave security area and if your DL flight is on time and does not waste time taxiing and waiting for a gate (which is the biggest problem at JFK in my opinion), then you should be fine. My guess is that, if this a single ticket, your luggage should transfer directly. so no worries there.
So, from T3 to T1, airtrain is very fast (next stop), and easy access, you would have to take the "all terminal loop" that run backwards:
http://www.panynj.gov/airtrain/
It runs on the inside tracks (like the peripherique interieur!)
You could also decide to walk on the side walk btwn T3 and T1 and zigzag btwn cars. It's pretty easy and fast, both terminals being very close.
Security at T1 in those late hours should not take too long. In any events, i can't remember the last time i was on AF009 and the flight was on time! so, you are most likely to get at least an extra 20-30 minutes.
A little tip: last time at T1, there was an empty lane to enter security on the right side (was looking for fast elite lane, but that was a regular lane, no status needed), whereas for some weird reasons, everybody was waiting in a long line on the left side... so i got in very fast!
Have a good trip!