Are you sure you mean Strasbourg, Germany? I've just checked a couple of books and can't find any listing for it - there's a Straslund, Germany up on the Baltic coast...or Strasbourg, France, which has been part of Germany on and off over the centuries, but at the moment is still in France. Makes a difference as far as travel times are concerned... Frankfurt and Strasbourg are both pretty close to Paris, Straslund would take a lot longer.
Nice is really a long way from anywhere in Germany, or from Paris for that matter, it would eat up a lot of time just getting there and back.
Generally three days is a good minimum rule of thumb for getting a flavour of a city, but some cities (Paris, London, Rome to name a few) really have so much to offer that you could spend a lot longer taking it all in. We spent about four days in Paris in June - it was enough to get a taste, but not nearly enough to see everything. I guess the thing is, you can see quite a lot in three days, but you won't be bored or disappointed if you stay longer - you'll just have more time to enjoy strolling in the parks or along the Seine, relaxing at a cafe or immersing yourself in the fascinating exhibits at the museums and galleries.
If you have the extra day on your pass to cover the trip to Versailles, that's great, otherwise, you can buy a local transit pass which covers at least a portion of the RER ride to Versailles. We bought the Paris Visite pass, which was okay, although a better deal is the Orange Card. Unfortunately, it's a pass valid for a calendar week and isn't sold on Thursdays (the one for the following week goes on sale on Friday). Naturally, we arrived Wednesday night, but didn't know about the restriction, so didn't buy the pass (or try to) until Thursday morning!
I think that pass pays off in about 10 rides, which is very doable even in three days, and totally worthwhile for a longer stay. Our pass took about 15 rides to pay off, which we easily accomplished in our three days of sightseeing there. Best thing is that you can use them on all bus, metro and RER lines within the valid zones (1&2 is enough for most visitors to Paris) so if it's hot, pouring rain or your feet hurt, you don't hesitate to hop on a passing bus instead of hoofing it to your next destination.
We mostly went to and from our hotel by metro, but took note of the nearest bus route and were very grateful on a hot, tired, hungry afternoon after wandering fruitlessly for about 2 hours, to stumble across a bus stop with our bus waiting there. Didn't quite say "HOME" but close enough!
The other thing is, by basing yourself in Paris for a longer stay, you can still daytrip to nearby places - Versailles, Chartres, even the Loire Valley, without the tremendous investment of transit time that a visit to Nice would entail, and with the added advantage of not having to lug all your stuff along with you.
The end of September will be a great time to visit Paris - may still have nice weather, but it won't be stifling, like now, most of the tourist hordes will have subsided and the local Parisiens will be back into their normal lives so you'll get a great sense of what life is really like there. It will also be a far less crowded time to see Chartres and Versailles, if that's what you choose to do.