So, as Thrifty Bill says, in order to convert this to a normal freewheel system you need an adapter that fits into the bottom bracket shell that will allow a modern 3-piece crank and bottom bracket to be installed. The Schwinn has a 1-piece crank and normal bottom brackets/cranks won't work without the adapter. Some call these American to European adapters (or something similar). I've never actually seen one of these, but pictures make it appear to be simple to install.

Then, you need an inexpensive crank set and bottom bracket. If you are in someplace flat, you might consider a single chainwheel in front -- someplace like Houston or Oshkosh, Wisconsin. Most people probably disagree with me on this.

Then, you need a new freewheel. Probably 5-speed unless you want to respace the wheel and re-dish and cold set or spread the rear. You have to get the old freewheel/sprocket cluster off. Most Schwinns of that vintage used an Atom, I think. An LBS should be able to remove it for almost no cost, or loan you the tool, or you can look at the cluster and figure out what tool you need and buy it for $5 to $10. A first guess is the Park FR-4 -- but check it.

All told, not a lot of money -- particularly if you can do the work yourself. Personally, I would do it if your fiance likes the bike. It's a nice, good looking bike in apparently pretty good condition and putting a couple bucks into it is well worth the cost, in my opinion.