Q:

Why can't helium nuclei (alpha particles) react with fluorine?

Alpha particles are basically just helium nuclei, so it will accept an electron pair to become stable. 
Will fluorine, being highly electronegative, not just donate an electron pair but form a bond with helium?

A:

Why, many atoms would readily create a bond with helium, when it comes in a form of alpha particle (just cooled down enough to chemically interact with). There is comparatively stable $\ce{HeH}^+$ and other similar particles, too. But a positive particle is not a compound yet. And when you try to form a compound out of it, that is, to balance it with some negative ions - well, that's where the problem arises. It would violently react with absolutely anything else, form some compound, and happily release the neutral helium atom.

