hi! As it happens, I just rounded up a bunch of posts on zeppelins and blimps (cuz, as it turns out, I don't know the difference) for a related post last week; check it out here:

• Were blimps ever seriously used in war?

I've not seen the film, but I doubt they're manned zeppelins. They're much more likely to be unmanned barrage balloons, which were an early way of providing a ground-based defence against low-flying aircraft. The balloons were tethered to the ground by thick, metal cables. Any aircraft attempting to fly through them would quickly find itself losing important structural bits, and having quite a bad day. They were placed around important strategic targets, and could even be carried by ships. Compare this image from the Normandy Landings, which clearly shows the balloons, to this still from the film.