Get the paternity test, and know for sure, and act accordingly.
Who cares how many people she's slept with, or why she waited? Assuming she's within the Statute of Limitations (if any), then the suit is timely. Her child needs shoes no matter who his or her father is, and a test will determine that for certain.
Do people ever lie on affidavits? Is the Pope Catholic?
Like I said, the test will tell the tale.
If the child is your fiancé's, then yeah, he's going to have to pay support, and probably back child support, too. He will also be able to sue for visitation rights. You might become a stepmother. And so it goes. If there is a biological connection, I hope that you and your man can love this child, who is innocent in all of this and did not bring this upon you, or anyone.
This sort of thing happens. Yeah, it's a shocker. But, fortunately, there are DNA tests these days. Consider what things were like 30 years ago - your fiancé could have ended up on the hook for a kid who wasn't really his. At least now, it'll be crystal clear.
BTW, I think you should tell both sets of parents. Prepare them for the fact that they might have a grandchild. And that there is a court case and there is a possibility that it could get ugly.
Recognize that your family might turn out to not look exactly the way you envisioned last week or last month or last year. But this family is no less valid, or less beautiful.
Get the test done.