Looking for best way to go from southhampton cruise port to paris

The fastest way will be flying. Flybe Airlines goes from Southampton Airport to both Paris Orly and Paris Charles de Gaulle. http://www.flybe.com/

Flybe. has flights from Southampton airport to Paris CDG for about $100 for a changeable ticket with 45 lbs maximum one checked bag.

Otherwise train to London then Eurostar to Paris.

A third option - not necessarily the fastest or the cheapest - is a ferry from Portsmouth (short train ride from Southampton, and lots to see), then a ferry Portsmouth to Le Havre and a train from there to Paris. Details here: www.brittany-ferries.co.uk/
A cross-channel ferry will be less glamorous than whatever you arrived at the cruise port in, and you may be fed up of boats by then.
I would suggest train to London and then Eurostar because it gives you an opportunity to have a few hours in London, otherwise direct flight from Southampton airport.

Looking for best way to go from Southhampton cruise port to Paris-any suggestions.

Define "best". Fastest? Cheapest? Most scenic?

Personally, I think going via private helicopter is hard to beat - especially if someone else is paying. But you may have other priorities...

Non-stop flights

7:15 am SOU
9:35 am ORY
FlyBE 3041
-.M.Tu.W.Th.F.Sa.

10:30 am SOU
12:45 pm CDG
FlyBE 3033
Su.M.Tu.W.Th.F.Sa.

6:20 pm SOU
8:40 pm ORY
FlyBE 3047
Su.M.Tu.W.Th.F.-.