Can I replace a 40A breaker with a 50A breaker?
REPLACE THIS PANEL NOW

Your panel almost certainly is suffering from breaker-to-busbar contact damage, rendering it a ticking incendiary device.

See this answer for the gory details on just what is wrong with FPE's "breakers".

If you post a picture of your panel (dead front off), I can determine if you can have your electrician install one of the Eaton retrofit kits (the kit itself is several hundred $, but it saves significantly on labor as the existing enclosure can stay in place) or if you need a total panel replacement (cheaper parts, but more labor).