IMO a dog door belongs in a solid door where it is really as out of the way as possible. As for the french doors have you thought about which way they will open they take up floor space no matter what and that is why often sliding doors are the best option. What have you been using up to now for a dog door? IMO the best look for the french doors is a panel on each side the same and the 2 center doors opening.. If you post some pics you migh get some other answers.

make the center pair of french doors as large as needed, add fixed sidelights, up to equal the size of the french doors.

Like mentioned, you could do a pair of 36" doors with sidelites.. This is the only example we have, ignore the design. Beautiful Bevels

I've seen us do 42" wide doors. With a wide enough stile, I think 48" is possible albeit a very wide door.. If you want glass, at top with a dog door, consider a half lite door or 3/4 lite door.