A wine class in Paris may be a good idea.
The best trip that could qualify as a convenient day trip is Reims, easily reached quickly by train, where you can tour a champagne house or two (massive places with underground caves holding thousands of bottles of wine) and back to Paris in one day.
As a stretch you could probably get to western Loire Valley where a local white wine is grown and bottled. It's not a convenient trip but may be doable.
For red wine, I think you have to plan for more than a day trip. Maybe somewhere in Burgundy would work? Beaune has a place in town that's high on Rick's list, but I don't know whether it's reachable from Paris as a day trip?