If we have a cap and two open ended inductors like this, how is the circle gonna oscillate?

it's not. An inductor with one end not connected (assuming an ideal inductor) will not have any effect on the circuit.

But the jumper wire across C2 has some inductance, as does the wires to the cap itself, and that can form a resonant circuit.

And inductors are never ideal, so the open ends of the inductors (and other parts of the inductors) have capacitance to other parts of the circuit, depending on the physical layout, and those can form resonant circuits.