The decision is easy, go to Paris.
1. With only 4 days annual vacation left, another long-haul is out of the question and you are so near right now.
2. I agree an experience shared is always better but at only 25 years of age you can lay down the corner stones for future visits with a more significant other. Time is on your side.
3. Never put off what you can do today, it saves so much time in the long run with needless backtracking.
Ok, did a different search this time and they do offer a 10 day initiary that I didn't see before, if you booked that you have time for Paris, on the 12 day one you arrive Venice on day 10 and go sight seeing on day 11, you can always skip that and go to Paris instead.

The decision is easy, go to Paris.
1. With only 4 days annual vacation left, another long-haul is out of the question and you are so near right now.
2. I agree an experience shared is always better but at only 25 years of age you can lay down the corner stones for future visits with a more significant other. Time is on your side.
3. Never put off what you can do today, it saves so much time in the long run with needless backtracking.
thanks, exactly what I wanted to hear!

Great Erica
Forget the Louvre..a huge time swamp
Do Museu d Orsay and Orangerie
Take a bateau mousse boat trip, included with the last Fat Tire ride
Use a day at Chrartres..fab medieval town, regular hour train ride from Gare Monparnasse
A special place
Hear a concert at St Chapelle or St Julien le Pouvre
Cluny Museum
Don't worry about being alone...you will find lots of nice people
Abientot

www.skyscanner.com You will see that flights from Italy to Paris can be quite cheap if bought well in advance. This site shows the one-way flights on European budget lines as well as the major carriers. The train would take far too much of your limited time.
Assuming you are flying trans-Atlantic, try to get a multi-city or multi-destination ticket, flying into Rome and home from Paris. It should be about the same price as Rome round-trip and will save the time and money of returning to Rome. Bye-bye to your group, of course, but by that time you all might be willing to go your own ways. As to weighing yourself down with loot, I travel to store up memories, not trinkets that only gather dust back home.
And don't worry about travelling by yourself! It'll be a great experience - you learn a lot about yourself, and it's really lovely being able to do what you want to do (just take the usual precautions, especially being careful with valuables on the Metro and at tourist sites). I second doing the d'Orsay and the Orangerie. Sainte-Chapelle should definitely be on the list.
Also, with 6 days to play with, you can have plenty of fun in the city and still be able to take a day trip or two out to see somewhere else.
And, you can always choose to stay at a hostel where you can meet other travellers with whom you can explore Paris.
Do Museu d Orsay
Take a bateau mousse boat trip
Use a day at Chrartres
Gare Monparnasse
St Chapelle or St Julien le Pouvre
As a rule of thumb, I would never take advice from people who can't spell the place they are recommending correctly. It's a clear sign of incomplete knowledge.

After 10 days in lockstep with your tour group, solo travel to Paris will feel like absolute freedom.
Because that's what solo travel is. Do what you want when you want for as long (or short) as you want.
Experiences, not things, make the best souvenirs. If you're buying for others, stick to fridge magnets and t-shirts.