No, the effects of Comprehend Languages and using your familiar's senses are mutually exclusive
Because the description of comprehend languages uses the word "you", it would appear that this does not extend to your familiar, as further supported by the fact that the find familiar spells says (PHB, pg. 240):
... you can see through your familiars eyes and hear what it hears until the start of your next turn, gaining the benefits of any special senses it has. During thus time, you are deaf and blind with regards to your own senses.
However, later in the description of Find Familiar, it says this (PHB, pg. 240):
Finally, when you cast a spell with a range of touch, your familiar can deliver the spell as if it had cast the spell.
Since comprehend languages has a range of "self, not "touch", the familiar cannot cast the spell, and thus the senses affected are yours, not the familiar's.
Since you are "gaining the benefits of any special senses it has" and are "deaf and blind with regards to your own senses", this would mean that since you are the one affected by the comprehend languages spell, and you cannot see or hear anymore, then anything the familiar sees or hears "for you" doesn't count as you hearing it, since your are deaf, or seeing it, since you are blind.
Therefore, you cannot understand languages through your familiar as you intend.