It is possible to send composite video and analog stereo audio over unshielded twisted pair (UTP) cables like Cat 6, although it is not a recommended practice, as they should be sent through coaxial cable.
Ideally you should use 3 baluns at each end. The video and audio are unbalanced signals and the UTP is balanced; the baluns will make a better match and give you better noise and interference rejection. Baluns degrade the signal quality a bit, but the tradeoff for noise immunity is probably worth it. There are modestly priced passive and more expensive powered (active) types available.
You can also try it "raw" (without baluns) but you should use 1 complete pair for each signal. If the blue/white pair is already in use for phone, the three remaining pairs may work for video and stereo audio, but be aware you may pick up an objectionable amount of hum, impulse noise, and phone line crosstalk, especially ringing signals. Pick a wiring convention and be consistent at each end. For example on each pair either the white striped or solid conductor can be"ground" (tied to the RCA outer shell) but it must be the same at each end.
This subject comes up fairly often so a search may yield some past threads with more specific experiences and advice.