We present the AGAPE astrometric and photometric catalogue of 1579 variable stars in a $14'$ $\times$$10'$ field centred on M 31. This work is the first survey devoted to variable stars in the bulge of M 31. The R magnitudes of the objects and the $B-R$ colours suggest that our sample is dominated by red long-period variable stars (LPV), with a possible overlap with Cepheid-like type II stars. Fits of the light curves with sinusoids suggest that a large fraction of the stars correspond to periodic or semi-periodic objects with periods longer than 100 days. Twelve nova candidates are identified. Correlations with other catalogues suggest that 2 novae could be recurrent novae and provide possible optical counterparts for 2 supersoft X-ray sources candidates observed with Chandra.