High-finesse optical microcavities are at the core of a wide range of scientific advances and technical applications from quantum technologies to optical sensors. Among them, fiber Fabry-Perot cavities (FFPCs) are of particular interest because of their unique properties. However, integrating FFPCs into photonic devices remains difficult because it is complex to individually tune their resonance frequencies. Moreover, integrating them in a miniaturized device is an experimental challenge prone to errors. To tackle this problem, we combined FFPCs with femtosecond laser manufacturing to create the very first integrated FFPC on a glass substrate. Post-assembly fine tuning is performed to maximize the finesse by actuating an integrated flexible mechanism. These integrated FFPCs devices pave the way to new scalable and miniaturized photonic sensors with extremely high resolution particularly interesting for quantum applications.