DM's call as to whether the familiar and caster can 'work together'
You attempt to interrupt a creature in the process of casting a spell...If it is casting a spell of 4th level or higher, make an ability check using your spellcasting ability. The DC equals 10 + the spell's level. On a success, the creature's spell fails and has no effect.
Presumably it is this ability check on which you would like advantage with the Help from your familiar. In this case, we have two issues; timing and eligibility to help.
Note that Counterspell is cast as a reaction on the turn of the caster whose spell you wish to counter. Thus, to be available to Help, your familiar would have to have previously Readied their Action to be one of Helping you when you cast Counterspell, and then use their Reaction to actually Help. Since Readied actions can only be used in response to perceivable triggers, the familiar would need to be able to know when you were about to begin Counterspell. If you have a telepathic bond that doesn't require an action on either of your parts to use, that should serve to alert them as a perceivable circumstance.
The requirements for "Working Together" are (PHB 175):
A character can only provide help if the task is one that he or she could attempt alone. For example, trying to open a lock requires proficiency with thieves’ tools, so a character who lacks that proficiency can’t help another character in that task. Moreover, a character can help only when two or more individuals working together would actually be productive. Some tasks, such as threading a needle, are no easier with help.
Here DM interpretation is required. A more strict DM could say that unless the familiar itself can cast counterspell, it can't Help since it couldn't attempt the task alone. Narratively, it wouldn't know where to begin or in what way it could actually aid its master.
A more permissive DM might rule that the Help required is the ability check only, not the spell itself, and of course the familiar can make an ability check using your spellcasting ability. Narratively, the familiar could be helping in identifying when the enemy caster is beginning to cast, perhaps what spell they are casting (as per the optional rule in Xanathar's), or other pertinent information that would assist you in defeating their magic.