The familiar would not see the illusion...
Phantasmal Force affects a single creature by creating an illusion 'that is perceivable only to the target'.
If a wizard with a familiar is targeted by the spell, then, as the wizard and his familiar (a conjured spirit) are not considered a single creature, the familiar would be unaffected.
Ceratinly no other part of normal play treats the wizard and their familiar this way. If, as a matter of course, you required a wizard's familiar to also save against any spells that targeted the wizard you'd find the familiar to be somewhat squishy?
...And it probably could help the wizard shrug off the effects
There's no explicit rules statements, specific to Phantasmal Force that we could apply here, however, I'd apply the general rule that the familiar, in just the same way as another party member might, could spend their action to take the help action to give the wizard advantage on their Investigation check.
When you take the Help action, the creature you aid gains advantage on the next ability check it makes to perform the task you are helping with, provided that it makes the check before the start of your next turn.
I'd also rule, though once again it's not explicit, that if the wizard used an action to:
'see through [their] 'familiar's eyes and hear what it hears'
... then they would not, for as long as they did so, see the illusion.
While it's explicitly the wizard's mind that is affected by Phantasmal force, the implication of the use of the plain English phrase which states that the wizard 'hear[s] what it hears' is that the wizard is also directly seeing what their familiar sees. It seems nonsensical to make the bizarre distinction that for some reason what the wizard sees through the eyes of their familair is distorted by the lingering effects of Phantasmal Force but that what they hear through their familiar's ears is not. After all the Phantasmal Force is as equally capabale of including sounds as it is visible phenomenom.
If the wizard spends an action to do this, I'd once again give them advantage on their subsequent Investigation check.
In both circumstances, (the familiar taking the help action or the wizard taking an action to borrow the familiar's senses) an additional action is being spent in order to grant advantage on the Investigation check - so it seems roughly balanced (though the wizard's action is probably worth more to the party as a consumable resource than the familiar's is).