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bottom locks on double door mechanisms
In which case its a shootbolt keep, which the shootbolt(s) engage into.
Some double French doors have single keeps for each side, whilst others have a double.
Theres probably one at the top of the door, which is inevitably in better condition to help finding an alternative.Treat the shoot bolts and mechanism to a clean and drink of oil, as once there's a new keep in place you could end up with it getting jammed if its nearly seized.
It was a "keep" of some description.
There's lots of options available, depending on the size of shoot bolt, Deadbolt that goes into.
https://www.google.com/search?q=Shoot+bolt+keep&tbm=isch&ved