There are several reasons why this is not at all a good idea.
1) Goldfish prefer water between 65 and 75, depending on species. Bettas prefer it to be around 78.
2) Bettas are not social animals and will probably nip the goldfishs' tails.
3) Goldfish, even the "small" fat round ones, get huge, to the size of baseballs. A betta could get nommed by mistake.
4) Goldfish prefer moving water, bettas prefer still water.
5) Goldfish produce massive amounts of waste. The minimum size for two smaller goldfish, like fantails, is a 30gal with a 60gal filter. 15 gallons won't even support one. Ideally, you should probably have at least a 55 gal before getting goldies.
Goldfish are beautiful creatures, but they are not compatible with bettas and are expensive, occasionally difficult creatures to keep.
Be careful of projecting human emotions onto your fish. Your betta is not actually lonely - bettas don't feel or think in the same way we do. Any tankmates that you add will be for your sake, not his.
Before deciding on potential tankmates, you want to know two things: water hardness and pH. For instance, tetras do much better in soft water with a lower pH, whereas livebearers will thrive in harder water with a higher pH. :)