As long as the antenna was designed to receive TV channels 2 through 6, the answer is probably yes. If the antenna looks anything like this one...
... then you're probably all set. It's those long elements toward the back of the boom that do the best job pulling in FM signals.
On the other hand, if your antenna has any sort of built-in amplifier -- particularly if the works are inside a plastic enclosure, and it needs power from a wall wart to work right -- be aware that many such models also include an "FM trap" designed to reduce interference to TV signals from nearby radio stations. These antennas will still pick up local FM stations, but the trap-and-amp combination can degrade sound quality badly.
Assuming you've checked your Antenna out as Don has suggested, and IF it will receive FM, then, here's a way to get all that done.
First of all, not only "should" you be able to receive FM, but HD Radio too.
It's something that many Audiophiles are really into !
As your cable comes into your HT Area, you can then route it to the... Winegard CA-8800 FM Separator
This gives you a Pass-through for your TV Signals, routing a Coax out of it, and to your FM Receiver.
Now, if you have a newer Receiver, the Coax will screw right on to the "F" terminal for the Antenna, or, if you have an older Receiver, use a... Matching Transformer
To convert the input to 300 Ohm on the two Terminals.
You may also need a couple short pieces of Coax to hook it all up.