Ultrahigh-resolution fiber-optic sensing has been demonstrated with a meter-long, high-finesse fiber Fabry-Perot interferometer (FFPI). The main technical challenge of large, environment-induced resonance frequency drift is addressed by locking the interrogation laser to a similar meter-long FFPI, which, along with the FFPI sensor, is thermally and mechanically isolated from the ambient. A nominal, noise-limited strain resolution of 800 f{epsilon} /sqrt(Hz) has been achieved within 1 to 100 Hz. Strain resolution further improves to 75 f{epsilon} /sqrt(Hz) at 1 kHz, 60 f{epsilon} /sqrt(Hz) at 2 kHz and 40 f{epsilon} /sqrt(Hz) at 23 kHz, demonstrating comparable or even better resolutions than proven techniques such as {pi}-phase-shifted and slow-light fiber Bragg gratings. Limitations of the current system are analyzed and improvement strategies are presented. The work lays out a feasible path toward ultrahigh-resolution fiber-optic sensing based on long FFPIs.