Re-enabling the Ubisoft overlay didn't cause the issue to re-appear, so I guess verification fixed it.

After verifying the game files via Steam (resulting in one file being reacquired) and disabling the Ubisoft overlay, this problem isn't appearing anymore. So one or both of these things together seemed to solve it.

When I start a race, a transparent image of the moment before "GO" stays on the screen for the duration of the race and after returning to freedrive and entering the pause menu. The afterimage goes away if I change resolution, but reappears upon starting a new race.