It's an interesting question since it seems the mythical "third great sci-fi franchise" always seems to be whatever happens to be popular at any given time. Certainly some franchises have had popular resurgences over the years, but nothing else in the genre it seems has had the staying power of those two. Even in the lull periods where no new movies or TV shows were being produced, Star Wars and Star Trek were still very much in the pop-culture awareness.
DOCTOR WHO matches the other two for breadth and longevity, although it took a bit more time becoming a widespread phenomenon in the USA, as opposed to overseas.
I did think of 'Doctor Who', but I sort of discounted it on the basis that (as I am given to understand) it's international popularity is relatively recent (VERY recent given it's 50 year history) and has yet to really stand the test of time outside the UK's borders.
Of course over here it never left pop culture, even for those of my age who mostly grew up in the lull years. I have only very dim memories of McCoy being on the air as back then I think I was more interested in He-Man and Ghostbusters. Still, everyone knew what a Dalek and Cyberman was and what the TARDIS looked like. But I'm not sure the same could be said for people of my age who grew up on the other side of the pond.
I've heard Who had a bit of a cult following in the states during the Tom Baker era, but that's all it was. A cult following. Nothing like the broad market appeal of Star Wars or Star Trek.
Mind you, even Trek wasn't that popular in it's time and only really took off in the 70's with the endless repeats.
If we go by amount of stuff made as part of the franchise I'd have to say it would be Stargate. It had one movie, a spin-off series with 214 episodes and two of it's own movies, a second series with 100 episodes, a third with 40 TV episodes and 34 webisodes. There have also been a whole bunch of books based on the original movie, and some for all three TV series, some comics based on two of the series, 3 video games based on the shows, a trading card game, an RPG, two video games based on the movie, and three amusement park rides.
I'm not sure that sheer quantity alone is a reliable metric. Ask most people on the street if the the word "Goa'uld" means anything to them and I'd be willing to bet most will just give you a blank look. Ask the same people if they know the word "Jedi" or "Spock" and you're likely to get a much more positive response.
The Highlander franchise has also (somewhat inexplicably) put out quite a bit of media over the years in the form of at least two TV spin-offs that I can recall, plus a cartoon, an anime movie, several theatrical sequels are a few...uh...other films.
Despite that (and even though I've always loved the first movie) I don't think anyone would put Highlander up there with the big boys.
If I had to place Stargate anywhere, it'd be about on par with the likes of Farscape, Firefly, Galactica & B5. Well known to the genre fans, not so much to the public at large.
I suppose in terms of public recognition, the 'Alien' franchise is probably the closest to Wars & Trek. Whether people have seen all the movies or not, I think most people know a xenomorph when the see one (even if they wouldn't necessarily call it by that label) and the second movie in particular seems to have spawned about a dozen fairly well known quotes.