Where exactly did we see Tsunade being the last living Senju? Since Senju was the strongest clan, there still has to be lots of Senjus in the present.
About Naruto's mother, lets assume she wasn't Senju since she was from different village. About Minato Namikaze, hmmm... let's see.
If i'm not wrong, japanese inherit theri surnames from their mother(see Naruto Uzumaki). So, we can say that Minato's mother is from Namikaze clan. What about his father? There comes the big question. He could have been a Senju or any other clan.
Again, lets focus naruto who has large amount of chakra. Considering the description of Senju, there's a great possibility that Naruto is a senju. Also, remember Madara saw 1st Hokage in Naruto, just like Kakashi saw Minato in Naruto, and Tsunade saw Minato & Jiraiya in Naruto. Madara also told Naruto that his fight with Sasuke was destined. (Senju v/s Uchiha destined).
So, my conclusion is that there is 99% chance of Naruto being a Senju.