If it says explicitly 50 ohm, I think that is a sign that you should better use 50 ohm cable.
However, in practical life on FM radio frequencies that doesn't matter much. You just can't pull out all the power through wrong cable to antenna. Due to mismatch you will have probably a bad standing wave ratio, which means that the energy your transmitter creates, bounces inside cable, warms it a bit and in serious case possibly damages the transmitter if the heat is too much. I say this in principle, knowing nothing about the particular transmitter and the coax and antenna. Possibly you would be safe, because 7w is not much, but low power is not a reason to be careless.
If you insist using that cable, you need a impedance transformer that changes 50 ohms output into 75 ohms.
More info is needed. If the tv antenna cable leads indeed to a TV antenna, you are adding problems to your setup. You really would need a FM antenna for 88-108 MHz. Otherwise you have a mismatch again.
Also, if you are talking about receiving central antenna system of apartment building and several tv receivers are connected to that system, transmitting watts into that system is a absolute no-no.
In the first phase one could test just with a telescope antenna of an old radio, place tx by the window and go out with a pocket radio to see what happens.