No. Photographic film does not have infinite resolution.

Film is limited by the size and distribution of its light-sensitive grains, along with the film’s overall modulation transfer function (MTF). Because film isn’t arranged in a neat pixel grid, its resolution is not best described as a fixed pixel count, but that does not make it unlimited.

In practice, as you enlarge a film image more and more, grain and noise become increasingly visible and eventually overwhelm fine detail. So while film may not have the same kind of hard sampling grid as a digital sensor, it still has a real limit to how much detail it can record.

Digital sensors also don’t translate perfectly from megapixels to visible detail, since actual resolving power depends on more than photosite count alone. So the fairest comparison is that both film and digital have finite resolution, just limited in different ways.