In a field of 1 degrees radius centered in the Coma cluster of galaxies, UV (lambda = 2000 Angstrom) observations with a 40-cm balloon-borne imaging telescope (FOCA) have provided a list of 442 UV sources brighter than m(UV) = 18, which are identified in the Godwin et al. (1983) catalogue. 254 are identified as galaxies, 178 as star-like objects and 10 as galaxy-star pairs, unresolved in the UV image. The 254 galaxies fall into two sub-groups. The galaxies brighter than b=17 define a sequence in the (b-r, m(UV)-b) color-color diagram which is well fitted by the models of Bruzual & Chariot (1993); most are cluster members. The galaxies fainter than b=17 show distinctly (m(UV)-b) colors bluer than the former group at the same (b - r); most of them are likely background late-type galaxies. Notably, a significant fraction of the 178 star-like objects have UV magnitudes and colors similar to that of the second group of galaxies; ground-based spectroscopy is required to determine their nature and/or membership. In the UV sample, 61 galaxies have radial velocities consistent with cluster membership. Among them, nearly half are blue (m(UV) - b < 1), star-forming galaxies. Their cumulated UV fluxes lead to a star formation rate of similar to 23 h(-2)M.yr(-1). Their velocity distribution shows an unexpected concentration near 7500 km s(-1) and a void in the 6000-7000 km s-(1) range. The other half contains red, galaxies (m(UV) - b > 1) with little or no recent star formation. All early-type galaxies brighter than b = 14.5 are detected in UV and have a median color (m(UV) - b) = 3.0 in agreement with the representative spectral distribution of an elliptical compiled from IUE. 17 early-types galaxies which have spectroscopic data in the sample of Caldwell et al. (1993) show a correlation between the (m(UV) - b) color and the H delta (absorption line) equivalent width; some, with (m(UV) - b) < 1, would imply that the last starburst event is younger than 1 Gyr or that a residual star-formation is still present. The median UV flux and the fraction of blue star-forming galaxies which are cluster members show an enhancement at similar to 25' (0.5 h(-1)Mpc) from the cluster center, suggesting that a global physical process might induce star formation in a rich cluster such as Coma.