Is a replacement fluorescent-tube light not working because it draws too much current?
Is the incandescent drawing too much current?


No.

If it was, the circuit breaker would trip. This would only happen in the case of a serious fault in the fixture (or incorrect wiring). You would probably know if a circuit breaker had tripped.

The largest two-tube fixture would be 2 x 6-foot tubes. That would be rated about 140W. On a 110 volt AC supply that fixture draws a current of about 1.3 Amps. Most circuits will be rated for a maximum current many times higher than that.