The beam-based alignment and feedback systems, essential operations for the future colliders, require high resolution beam position monitors (BPMs). In the framework of the European CARE/SRF program, a reentrant cavity BPM with its associated electronics was developed by the CEA/DSM/Irfu in collaboration with DESY. The design, the fabrication, and the beam test of this monitor are detailed within this paper. This BPM is designed to be inserted in a cryomodule, work at cryogenic temperature in a clean environment. It has achieved a resolution better than $10\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ and has the possibility to perform bunch to bunch measurements for the x-ray free electron laser (X-FEL) and the International Linear Collider (ILC). Its other features are a small size of the rf cavity, a large aperture (78 mm), and an excellent linearity. A first prototype of a reentrant cavity BPM was installed in the free electron laser in Hamburg (FLASH), at Deutsches Elektronen-Synchrotron (DESY) and demonstrated its operation at cryogenic temperature inside a cryomodule. The second, installed, also, in the FLASH linac to be tested with beam, measured a resolution of approximately $4\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ over a dynamic range $\ifmmode\pm\else\textpm\fi{}5\text{ }\text{ }\mathrm{mm}$ in single bunch.