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Fast radio bursts (FRBs) are bright and very short flashes of radio waves. They form a new class of astrophysical transients whose origins are currently a mystery. Among the several dozen FRBs discovered today FRB121102 is the only one showing a repeating activity and identified at sub-arcsec precision on the sky. Its bursts appear clustered in time with a cyclic activity several weeks long hence allowing multi-wavelength follow-up. To identify a possible high energy counterpart of FRB121102 when it is active at radio frequencies we propose a 3 orbits INTEGRAL ToO coordinated with a 50 ksec X-ray observation with XMM-Newton (within this common call).We will trigger the ToO when radio bursts will be detected in at least in 2 over 3 one hour long successive observations thanks to the regular daily monitoring of FRB121102 we are currently carrying out with the Nancay Radio Telescope (NRT). Prompt observations with Arecibo and Effelsberg will corroborate the NRT monitoring and then secure a good temporal coverage during the high energy survey.The vast collection of FRB theoretical model so far proposed includes the collapse of an accreting neutron star (NS) or a black hole (BH) giant radio pulses from pulsars giant flares from magnetars NS-NS/NS-BH/BH-BH binary mergers or interaction of asteroids with a highly magnetized pulsar. Assessing the low and hard X-ray emission associated to FRB121102 will tightly constrain the emission processes at play and the nature of the central engine powering these mysterious events and provide clues on their interaction with the surrounding environment. [truncated! Please see actual data for full text]