Feuilleter is what’s known as a stem-changing verb. There are about 100 in French – they all end in -er, and they fall into several categories – some double the letter, some add or change an accent (e.g., lever – je lève), and some have a minor spelling change (nettoyer – je nettoie).
But for all of them, in the present tense, it’s only the singular conjugations and the third-person plural that have this stem change. It is because of pronunciation: the stem change is required when the e in that syllable is pronounced [ɛ]. In the 1st and 2nd person plural, the e is pronounced [ə] and therefore there is no stem change.
Yes it is related to the pronunciation of the word : “Feuilleter” follows the same rules than the verbs that end with “eler” and “eter”.
In order to have the sound “è” the consonant “l” or “t” is doubled.
No verbs from the second group follows this rules.