I have seen two movies based on this work (The Time Machine (2002); and Time After Time (1979)). Neither has too much in common with Well's original story; however, the 2002 movie not only shares the exact title, it, like the book, has a library. The movie boasts a librarian as well: Orlando Jones Vox #NY-114. According to the Librarians in the Movies Filmography webpage Jones Vox is
a very cool virtual librarian of the future who is the compendium of (no less than) All Human Knowledge. He describes himself as a "third generation fusion card photonic with verbal and visual link capabilities connected to every database on the planet." He does a reference interview and even holds story time for kids. We first encounter him in 2030, then later about 800,000 years into the future (although his source of power is never explained).There is nothing quite so groovy in the book, the futuristic library is only mentioned one time, and there is no librarian in the dusty, deserted place. However, the hallowed space is given a bit of a build up, and is located in a place the Time Traveler calls The Palace of Green Porcelain (emphasis mine). What appears at first to be a museum of archaeology the Time Traveler discovers, to some delight, that it also "possibly" contains "historical galleries; [and] ....even a library!" Which he says "would be vastly more interesting than this spectacle of old-time geology in decay."
I saw Time After Time over 30 years ago, and I remember the gist (Jack the Ripper escapes into the future with H.G. Wells in hot pursuit), but I cannot recall if there is a library or librarian. I have added this to my Netflix list and will update this post, if necessary, once I have watched it again.
A free e-book available at Project Gutenberg.