I'm not an expert on Frankfurt itself. You could theoretically insert 23 hours on the ground there and go exploring. My personal take: I'd just insert about 4 hours on the ground there, enjoy the First Class Terminal for a while, and then move on to Paris.

Coming home, reverse the search process. Start your search for FRA-, MUC-, ZRH-, and VIE-SFO. If you intend to end up in any kind of major city, you can always search from there and see if there's a United flight directly home. Figure out what the best set of TATL options are for your homeward bound date, and then search for the accompanying short-haul Star Alliance flight to that point. You can have up to a 23-hour connection on a one-way award so if you're looking at 8AM TATL departures, just fly to the European gateway the day before. MUC or VIE would be a fun place to spend a day anyway.

In the middle of your trip, you might end up buying a separate one-way ticket (which should be cheap). For example, if the 2nd city in your itin is Rome, you probably have to buy Paris-FCO on Skyteam or some low-cost carrier. On pre-merger UA, you could do a stopover within a round-trip award, but the stopover city had to be a logical routing within Star Alliance. I've done one with Munich as a stopover, routed through FRA (for the FCT, of course!).