Are you sure they're 26"? Stock on Free Spirit 10 speeds should be 27" wheels. 700c is an easy swap, and you should be able to adjust the brakes and pads down to the rim.

If they are 26", know that a rim that uses fractional-size tires (i.e. 26 x 1 3/8) is a different size than 26" wheels that use decimal sizes. You should be able to go this route, but if you want a front brake (you do) you'll need to get a modern, longer-reach brake with some adjustability. The current brakes probably won't adjust down enough.