I would think the HFC is a better bet. It will also give you 50% or so off all local buses, trams etc in the towns you visit and some discounts on téléphériques and mountain railways as well. The GA is very expensive and you would have to do an awful lot of travel to "spend" the cost of it. Bern is so centrally located your train trips are not going to take forever nor be very expensive.
Paris is certainly do-able on a weekend. IF you can get going on the Friday night and get to work a bit late on the Mon am then that is even better. Travel via Basel - one hour to Basel and then 3 to Paris. But plan your time very carefully in Paris. Try and focus on a few major things that are close together. Paris is huge... and if you make a list of what you want to see, then look at a street map and localise them, then a Métro map to see how you get from one to the other you will save time once there.