We were in Paris for about a week last Fall. LOVED it.
Things we did right:
Bought a 5 day museum pass. It probably only saved a little $$, but it allowed us to skip the purchase lines, and only wait in the security lines. We also visited a few lesser known sites we would have never paid extra for, and some of these were great!
Bought the Metro pass (only works well if your week starts the same as the pass).
Downloaded the ‘out of the line’ app for the bell towers of Notre Dame (I think this was called JeFile). This allows you to add your name to the queue line early in the am for a timed entry, and skip the wait. It is a long (and narrow) climb to the towers, so skip if anyone in the group is claustrophobic.
Brought comfortable shoes! Far more fun to walk everywhere than use the Metro. Spent mid afternoon sitting in various gardens: some famous, and other small neighborhood delights. A needed respite, and wonderful people-watching opportunity.
Visited Versailles backwards (started in Marie Antoinette’s domain first thing in the day, when it was virtually empty, then worked our way toward the Chateau for a 4pm entry when the crowds started to thin.
We split our accommodations, and stayed in both the 4th & north end of the 15th arrondissements. It was a nice way to experience different neighborhoods.
Things we would do differently:
It was hard to match our dinner time with the French. We prefer to eat 5-7pm. That’s social time for the French, and most bistros were extremely crowded with locals, primarily for drinks. Dinner is much later. We also didn’t do enough research regarding places to eat prior to the trip. DH prefers to ‘discover’ places en route. I prefer to choose several well-rated (not necessarily expensive) places in advance. We choose the former option on this trip, and as a result I felt most of our meals were just so-so, which seems a shame in Paris! We’ll have to go back 
