Buy the art museum combo ticket online ahead of time to save money.
Don't do this on a Monday or a Tuesday as one museum is closed on each of those days.
You can do this anytime of the year. Late spring is the prettiest time of year in Paris with all the spring flowers in full bloom. Summer is very crowded and hot; be prepared for lots of tourists and be mindful of scam artists during this time of year.
Museums are free the first Sunday of the month, but are also more crowded that day.