Small jumps shouldn't hurt (like little hops), but if he is still young (under 3 years) he shouldn't be jumping any real jumps, not sure what you jump him over though so just a warning. His bones aren't fully developed and he can hurt his growth and cause issues in the future. This is for any dog. I have seen basset hounds compete in agility before, but they are usually on the lowest jumping height due to their size and length when they have reached adult age.
I haven’t had him jump over things, just up onto his hind legs to reach for a treat. His hind legs never leave the ground (excluding falling on his bum today)
I’m not sure if that sort of jumping would be equally problematic? Regardless, I think I still might avoid it with him, if only out of concern of him falling like that again