If we stretch the definition of "continental Europe" a bit to include the Canary Islands, a spaceport on Gran Canaria would have a bit over five thousand kilometers of useable range over the Sahara Desert, most of which is somewhat sparsely populated:
If we can get permission for the track to cross over the Nile Valley, the amount of useable range increases dramatically, as we can now continue over the Arabian Desert, Indian Ocean, and northern Australia, for a total of over seventeen thousand kilometers:
The main concern would seem to be the initial portion of the trajectory, over the northern Western Sahara (short track) or southern Morocco (long track), where avoiding overflying cities or large towns would require confining launches to a set of fairly-narrow launch corridors (especially for the more-northerly launch azimuths used for the long track), and likely also involve paying one or both of the national governments involved (depending on whether we're using just the short track, just the long track, or both) to buy out a few small inconveniently-situated settlements sitting under the launch corridors:
The restrictions on allowable launch azimuths would require flights targeting certain inclinations to perform a dogleg maneuver after clearing the restricted-azimuth zone; however, as this is very early in the flight of any orbital rocket launched from Gran Canaria (and, thus, occurs while the vehicle's speed is still fairly low), and because it should be possible to lay out launch corridors for a fairly-wide range of inclinations (ensuring that most target inclinations will at least be close to an allowable launch corridor), the Δv losses from this should be low to minimal.
A secondary concern (for the short track only) would be southern Algeria, where short-track launch trajectories pass near or over moderately-sized population centers in the Ahaggar Mountains:
However, the area in question is far enough downrange that this can probably be managed by arranging to alert communities in the area in advance of a launch and agreeing to pay out compensation in the unlikely event that someone's house or livestock are damaged by a falling rocket (like Russia does).