The 'Additionally' part of the next sentence seems to imply that they are bound to the same rules
From the SRD, here is the text of the spell:
While your familiar is within 100 feet of you, you can communicate with it telepathically. Additionally, as an action, you can see through your familiar's eyes and hear what it hears until the start of your next turn, gaining the benefits of any special senses that the familiar has.
Emphasis mine. The addition of 'Additionally' to the start of the sentence implies to me that the previous sentence needs to be taken into account. For instance:
Thanks for agreeing to watch my dog this weekend! While I'm away feel free to watch my TV or use my WiFi. Additionally, you can eat whatever is in the fridge if you get hungry
To me, that sentence implies you can eat anything from the fridge while you're watching my dog this weekend. I didn't give you carte blanche to take whatever you wanted from my fridge from this day forward, I simply gave you permission to eat from it at a specific time. If you walked into my house 3 months from now and started raiding the fridge, that wouldn't be what I intended above even though technically I did tell you you could do it.
DnD 5e seems to defer to a standard-english reading of most passages as a pseudo-ruling by default, so since we can make a pretty strong argument that 'Additionally' depends on the conditions in the previous sentence, I think we can be reasonably certain that you need to be within 100 feet for you to see and hear through your familiar.