I can't resist adding our experience. We have been fortunate enough to take more then one British Isles cruises over the years. We have seen some interesting, unexpected events altar travel plans for others. One event was an unexpected strike in Le Have. There was a large group expecting to disembark there and head to Paris. Their plans didn't happen.
We did our most recent cruise from Southampton in 2019. We had been to Paris but wanted to revisit. We flew from the U.S. to Paris, stayed 4 nights then took the Eurostar from Paris to London, where we spent several nights. Our high point was seeing the show "Hamilton" at the Victoria Theatre. We took National Express from London to Southampton leaving from Victoria Station. This is our usual way of getting to Southampton....very reliable and inexpensive, as many have mentioned.
Mostly, we caution people about a short visit to Paris, if it is your only time to be in that fabulous city...too much to see and too much to do. Hope your plans work out.