Private transportation to Paris from Le Havre

We have an overnight in Le Havre this June and are planning to spend the two days in Paris. We'd prefer private transportation than the train in order to maximize our time in Paris. Can anyone recommend a company who does this kind of thing? I'm having a difficult time finding such a company. I'd appreciate any help!

Also, respectfully, I do understand two days is not enough time to see all Paris has to offer. However, we've made up our minds and want to the best with the time we have in Paris. We have another port call in Cherbourg where we will visit the D-day beaches, so for this post, I am really interested in recommendations for transportation to Paris. Thank you! :)

We have never found any kind of private transfers in Le Havre. However, there always seem to be a few taxis in queue at the port.....any of which would take you to Paris for several hundred Euros. It is about 125 miles from Le Havre to Paris which means any private transport/taxi must drive over 250 miles round trip (even if they have to return empty). This is time consuming and very expensive. You could possibly save some time (from using the train) by getting yourself a one-way rental car....but once you factor in getting the rental car agency plus paperwork...not sure this saves much time. There is one rental car company at the port (rentacar.fr) but not sure they do one-way rentals...

Hank