The only thing I can think of is a play on the word 'trip' which can also mean to stumble and possibly fall. i.e. I was walking along and tripped on my own shoelace and fell over.

The joke, as written is not good. Slightly better, but still not great:

I had a trip last week.

Oh no! Did you hurt yourself when you hit the ground?

The problem with the original joke (ignoring the bad word play) is that 'trip to Paris' unambiguously points to the meaning of trip and it CANNOT mean stumble and/or fall.

Vince, thank you very much!

I think, this is somehow connected with the word "trip", but I am not sure

I don't get it 🧐🤔

Unless there is some specific pronunciation that match something "shameful" in another language...

Like: Michael Caine --> mycocaine