I was hoping to find a way to have door open and have some kind of mesh material that seals it up and vent attaches to that.

I don't want to make a hole in the wall. Right now I have it venting through the floor vent.

I cannot think of anyway possible to do this on a french door shy of replacing one piece of glass with plywood or something similar.

Is this a heat vent you are venting it to? I cant even imagine that would be a very good idea.

Ya but we don't use the heater

Does this room have a window?

"Ya but we don't use the heater"

Is it still hooked up? You very well be pumping moisture into your heating system making for a potential mess.

Are you renting the house?

Mold in the vents is also a possibility.

If you have a window, raise it enough to put a piece of plywood with hole in it for the a/c exhaust.