Context. The large number of ongoing surveys for pulsars and transients at various radio observatories is motivated by the science obtained from these sources. Timing and polarisation analysis of relativistic binaries can place strong constraints on theories of gravity. The observation of a growing number of millisecond pulsars (MSPs) spread over the celestial sphere may allow the detection of a stochastic gravitational wave background arising from supermassive black hole binaries. A more complete sample of young pulsars improves our knowledge of neutron star birth and evolution. Transients such as fast radio bursts can serve to probe the intergalactic medium. Aims. The SPAN512 pulsar survey covers intermediate Galactic latitudes using the L-band receiver of the Nançay Radio Telescope (NRT). The survey covers 224 sq. deg. of the sky for a total exposure time of 2200 h. Population syntheses predict the discovery of 3 to 19 new normal pulsars and a few MSPs. Methods. We present detailed modelling of the NRT beam with its L-band receiver and its sensitivity which we used to precisely assess the expected survey yield. We used the flexible Pulsar Arecibo L-band Feed Array data processing pipeline to search the 47 TB of SPAN512 data for pulsars and transients. Results. The SPAN512 survey discovered two new MSPs and one new middle-aged pulsar. We focus on the analysis of the 2.4-ms spin period pulsar J2205+6012 for which we also report the detection of gamma-ray pulsations. Its narrow pulse width (35µs at an observing frequency of 2.55 GHz) allows for sub-microsecond timing precision over 8 yr, with exciting prospects for pulsar timing array programs.