[dmichulke]

Not an etymologist, but I think they still have a common ancestor (proto Indo-European?). Lots of words in Latin with p have an equivalent with f in the Germanic languages:

Pater - father

Pes - foot

Primus - first

Note the English word is not necessarily the closest to the Latin one.

P and f are also considered the same sound in a few word distance metrics such as Soundex for the very same reason.

[thaumasiotes]

Yes, having a common ancestor is what "cognate" means. (Technically, in normal usage, "cognate" refers to words that (1) have a common ancestor and also (2) mean the same thing.) To use the familial metaphor, you descend from your mother, grandmother, great-grandmother, and so on, but you are cognate with your niece, cousin, aunt, great-aunt, etc.

"Foot" and "pes" both descend from the same Indo-European root, but the English word has no influence from the Latin one. Compare "pedestrian", which uses the Latin root directly.

[smallnamespace]

In fact, the pattern you noted is so distinctive of Germanic that linguists have actually given it a name:

https://en.wikipedia.org/wiki/Grimm%27s_law#Examples

The first part of the law is a general stop to fricative pattern, so not just p->f, but also t->th, k->h, etc.

[idontpost]

Yes, but Latin still isn't the root. PIE would be.