A good rule of thumb: Rules are supposed to mean something
Sometimes a rule is so poorly worded that part of it, in fact, doesn't mean much (or mean anything at all). But in general, writing rules like this takes a lot of time and effort, and that means someone had to get paid for it. It's probably supposed to mean something (even if that something sometimes is 'repeating what was said somewhere else, because it's also relevant here and someone might forget/miss it').
So you shouldn't even consider option #3 until you are very sure option #s 1 and 2 can't work.
Option 1 can likely be ruled out
The description for the Elf's "supernatural patrons" feature explicitly says elves get two spells for free. This is also explicitly mentioned in the description of the elven version of the "Magic" feature - which says they randomly know spells like wizards do, except they always know those two specific spells.
If in one place, the rules explicitly call out something like this happening, it's usually a good idea to assume they'll always call it out in the same way.
Furthermore, the spell list has a note saying that if a wizard rolls either patron bond or invoke patron, they learns both spells for the price of one spell slot. This would be completely meaningless if wizards got the spells for free implicitly, because they were mentioned in a feature.
In other words, because the find familiar description does not say 'wizards get the spell automatically at first level, in addition to their other selections', that means it doesn't work that way.
Option 2 has support in the text
The find familiar spell is called out specifically in a feature exclusive only to the wizard class. Only 3 spells get the special treatment of being called out by name in either the wizard or elf class. This supports the idea that find familiar gets special treatment.
This is still ambiguous
So, what does happen if an elf rolls find familiar? The rules (at least, the version Google found marked 'beta') do not say. The wording implies that elves can't have familiars, but they could explicitly spell it out, and they don't.
But from an in-story perspective, it doesn't make a lot of sense an elf would even want to bother with the spell. The supernatural patrons feature makes it clear the fact elves live for a long time has a big impact on their spellcasting.
This will interact very poorly with find familiar, which has a net loss to the caster of the familiar's HP total, when said familiar dies. From the perspective of an elf, as opposed to a wizard, this is probably rather inevitable.
The most reasonable interpretation is that no elf would ever want or bother to learn find familiar, and therefore any elf PC who rolls it simply rolls again.