  We present GALEX far-ultraviolet (FUV, $\lambda_{eff}$=1538 \AA) and
near-ultraviolet (NUV, $\lambda_{eff}$=2316 \AA) surface photometry of 40
early-type galaxies (ETGs) selected from a wider sample of 65 nearby ETGs
showing emission lines in their optical spectra. We derive FUV and NUV surface
brightness profiles, (FUV-NUV) colour profiles and D$_{25}$ integrated
magnitudes. We extend the photometric study to the optical {\it r} band from
SDSS imaging for 14 of these ETGs. In general, the (FUV-NUV) radial colour
profiles become redder with galactocentric distance in both rejuvenated ($\leq
4$ Gyr) and old ETGs. Colour profiles of NGC 1533, NGC 2962, NGC 2974, NGC
3489, and IC 5063 show rings and/or arm-like structures, bluer than the body of
the galaxy, suggesting the presence of recent star formation. Although seven of
our ETGs show shell systems in their optical image, only NGC 7135 displays
shells in the UV bands. We characterize the UV and optical surface brightness
profiles, along the major axis, using a Sersic law. The Sersic law exponent,
$n$, varies from 1 to 16 in the UV bands. S0 galaxies tend to have lower values
of $n$ ($\leq5$). The Sersic law exponent $n=4$ seems to be a watershed: ETGs
with $n>4$ tend to have [$\alpha$/Fe] greater than 0.15, implying a short
star-formation time scale. We find a significant correlation between the
FUV$-$NUV colour and central velocity dispersions $\sigma$, with the UV colours
getting bluer at larger $\sigma$. This trend is likely driven by a combined
effect of `downsizing' and of the mass-metallicity relation.
