What kind of lock can I put on a pair of internal French doors?

The surface bolts (that's what they're called) that iknow is talking about are an excellent way to lock them from one side. They work even better when they are installed at both the top and bottom. You can get them in finishes to match the hardware on the door. If you are looking for a secure lock, You can drill out the top and bottom of one of the doors and install flush boles. Same principle, but they go on the edge of the door. Then, on the other door, You would install a knob or deadbolt of your choosing, as triad mentioned. It all depends on whether you are looking for privacy or security. Hope this helps.

Double sided deadbolt. With glass close to the lock someone could break the glass and turn the lock. With a double sided deadbolt you need a key for both sides...So remove the key from the inside. I have seen people who leave them in the lock. Hope that is what you were looking for.

I also have internal french doors in my home. We used a slide latch Installed vertically, at the bottom of the door. Sliding it in to a hole in the floor. After painting we had to remind ourselves the doors were locked till we got used to it. The locks are really not that noticeable at all.

Hope this helped :)