We report on a simple fabrication technique for Fabry-Perot (FP) sensors formed by a microbubble within a polymer drop deposited on the tip of an optical fiber. Polydimethylsiloxane (PDMS) drops are deposited on the tips of standard single-mode fibers incorporating a layer of carbon nanoparticles (CNPs). A microbubble inside this polymer end-cap, aligned along the fiber core, can be readily generated on launching light from a laser diode through the fiber, owing to the photothermal effect produced in the CNP layer. This approach allows for the fabrication of microbubble end-capped FP sensors with reproducible performance, showing temperature sensitivities as large as 790 pm/°C, larger than those reported for regular polymer end-capped devices. We further show that these microbubble FP sensors may also prove useful for displacement measurements, with a sensitivity of ∼5.4 nm/µm.