The value of Fey Ancestry is roughly half a stat score 1, which will hardly unbalance anything.
In particular, adding that to a friendly creature is even less harmful. Giving it to a foe might increase its CR (probably won't as well), and certainly will make the encounter harder for low level parties, where it's usual for the Spellcaster to rely on sleep as their major utility spell. For friendly creatures though, how often will the familiar be targeted/affected by sleep or charms? My experience says: seldom. And I frequently put spellcasters against my parties.
1 There is a reddit guide on homebrew races (link to google docs) that ranks racial features using an ability score as the unity (e.g., +1 Dex = 1 point). From my experience, this guide was well received and I use it commonly to get feedback for my own homebrew races (although I don't use it to design them). There are other guides that do the same thing, e.g. this one (link to google docs). This one handles different ASI better (e.g. +2/+2 is as good as human +1 for everyone, which is a net +6). Both of them rank the Fey Ancestry feature as half a stat, as I described. That's my personal value for it, as well. Since the time this answer was posted, the guide has been updated. The conclusion of the answer did not change, though.