In this Letter, a long-range optical fiber displacement sensor based on an extrinsic Fabry-Perot interferometer (EFPI) built with a strongly coupled multicore fiber (SCMCF) is proposed and demonstrated. To fabricate the device, 9.2 mm of SCMCF was spliced to a conventional single-mode fiber (SMF). The sensor reflection spectrum is affected by super-mode interference in the SCMCF and the interference produced by the EFPI. Displacement of the SMF-SCMCF tip with respect to a reflecting surface produces quantifiable changes in the amplitude and period of the interference pattern in the reflection spectrum. Since the multicore fiber is an efficient light collecting area, sufficient signal intensity can be obtained for displacements of several centimeters. By analyzing the interference pattern in the Fourier domain, it was possible to measure displacements up to 50 mm with a resolution of approximately 500 nm. To our knowledge, this is the first time that a multicore fiber has been used to build a displacement sensor. The dynamic measurement range is at least seven times larger than that achieved with an EFPI built with a conventional SMF. Moreover, the SMF-SCMCF tip is robust and easy to fabricate and replicate.