From your list, I chose Lord of The Rings, mainly because I thought the first film was outstanding, I liked the second one a lot but the third was overly long and tiresome. I've not seen the Hobbit movies having been put off by being made near comatose after watching Return of The King.
My favourite film franchise is probably Terminator because Terminator 2 is one of my all time favourite films and The Terminator is almost as good. The subsequent Terminator sequels are watchable but not great.
Harry Potter is probably the film franchise that was most consistently good over the course of all the films in the series and I also rate the Planet of the Apes films very highly, going back to the original in 1968 to the most recent, Dawn of The Planet of The Apes in 2014
Overall 5 series comes to my mind:
Since Terminator & Alien are not in the poll, I have to pick 1 of the remaining 3.
As a franchise I must say Jurassic Park is probably the best overall. But I'm physically unable to vote against JAWS...