So my advice to you is to get off your duff and make your way to Auteuil as soon as possible, or at the very least sometime this spring when the outdoor gardens will begin to bloom in earnest. What's more, entrance to the greenhouses is free and open 364 days a year (Christmas excepted) from 9:00 am to 4:45 pm.
And here's a hot tip: in the biggest greenhouse known as the Palmarium, there are tables and chairs just waiting for you to come have a picnic. It's strictly BYOB (and for that matter everything else too) but absolutely allowed. Doesn't that sound better than a cup of crummy Parisian coffee on a terrasse filled with smokers?