After looking for swinging door latches and finding nothing, I installed a catch system on a pair of french doors leading from a bedroom to a bonus room using super magnets and hot glue.
How to Install A Magnet Door Catch System:
1. For a single door, drill holes in the sides of the door facing the door frame (or second door, if using two doors) using a wood-boring drill bit the same diameter as your magnets. Drill the holes only slightly deeper than the thickness of your magnets.
3. Glue magnets inside the drilled-out holes using a hot glue gun. BE SURE TO HAVE NEGATIVE AND POSITIVE SIDES OF THE MAGNETS FACING EACH OTHER. That is, if the positive side of the magnet is showing on the door, glue the “negative side out” on the door frame.If you have negative facing negative, your doors are going to bounce open all the time.
Use as many magnets as you wish to get the strength of catch that you want. I used three sets of super magnets, and the french doors stay closed if left undisturbed, but can be pushed open by a determined cat. I could add more magnets if I wanted to keep the cat from coming and going through the doors.