Originally Posted by
kaipoman
Europe as a whole is new to me so I pretty much want to go everywhere.

Then don't ruin your first trip by trying to do it all at once!
The earlier advice is sound - stay in Paris and skip Zurich altogether on this trip. Personally I would spend the entire time in Paris but if you absolutely must leave the city, I would suggest an easy day trip on only one of your days. Brussels is an easy high speed train-ride from Paris and can be done in a day. This may satisfy your desire to see another country/city on this trip. You can easily go up in the morning (take your coffee and breakfast on the train) for a nice afternoon lunch and stroll around the Grand Place and then be back in Paris for a late dinner.
Have fun!