Connecting circuit with two hots to breaker(s)
It's known as a multi-wire branch circuit, and it's perfectly legit.  The two ungrounded (hot) conductors terminate at breakers on opposite legs of the service, and share a grounded (neutral) conductor.

Since it's 14 AWG wire, you're correct that they should be 15 ampere breakers.

Do not connect both wires to the same single pole breaker.