A lot of people have probably looked into similar idea already. Launch is the most energy intense part of a flight. Hybrid aircraft might become commercially viable soonish. My idea:
A winch, that
Pase 1, pull: pulls an airplane along the runway like a glider winch launch (might also skip this phase if that enables the cable to be lighter)
Phase 2, power: stays connected and provides electrical power to the plane through a high voltage cable for as long as possible. During this phase the airplane would accellerate as hard as possible.
Phase 3, return: decouples from the plane and returns in a controlled way, using a chute, drone or smth.
A lot of variations are imagineable.