Context. High-contrast imaging is a powerful technique when searching for gas giant planets and brown dwarfs orbiting at separations greater than several AU. Around solar-type stars, giant planets are expected to form by core accretion or by gravitational instability, but since core accretion is increasingly difficult as the primary star becomes lighter, gravitational instability would be a probable formation scenario for still-to-find distant giant planets around a low-mass star. A systematic survey for such planets around M dwarfs would therefore provide a direct test of the efficiency of gravitational instability. Aims. We search for gas giant planets orbiting late-type stars and brown dwarfs of the solar neighbourhood. Methods. We obtained deep high-resolution images of 16 targets with the adaptive optic system of VLT-NACO in the L band, using direct imaging and angular differential imaging. This is currently the largest and deepest survey for Jupiter-mass planets around M-dwarfs. We developed and used an integrated reduction and analysis pipeline to reduce the images and derive our 2D detection limits for each target. The typical contrast achieved is about 9 mag at 0.5 and 11 mag beyond 1 . For each target we also determine the probability of detecting a planet of a given mass at a given separation in our images. Results. We derived accurate detection probabilities for planetary companions, taking orbital projection effects into account, with in average more than 50% probability to detect a 3 M Jup companion at 10 AU and a 1.5 M Jup companion at 20 AU, bringing strong constraints on the existence of Jupiter-mass planets around this sample of young M-dwarfs.