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My 1948 RCA projection set uses the same antenna scheme. About 10' of wire makes a decent radio antenna for both hands.
The FM band is smack dab in the middle of the VHF TV band between channels 6 and 7 so any TV ant that covers all of the VHF band will do FM. They probably built the AM section with an RF amp and enough sensitivity and correct antenna coupling to tune AM fine off of a TV/FM only antenna.
If it were me I'd get a good FM ant (I'm partial to folded dipoles for FM) and an antenna combiner (splitter with its inputs and outputs reversed is the same thing) and hook my video source and FM ant up.
If the TV is on its own chassis then it probably sends a 300 line to a switch on the radio (or vice versa) so if you wanted you could simply modify the set to split them into 2 antenna inputs. One for radio and a separate one for TV.
I typically use an agile modulator to transmit TV wirelessly throughout my property so for my RCA I'm just going to use a single antenna that is great for FM and good enough for TV and call it good (AM will grab a signal off any old piece of wire so I'll let it take care of it self).
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