Camera film is puny compared to the basilisk stare.
There is some precedent for lethal spells doing damage to physical objects. For example, when Dumbledore and Voldemort do battle in the Ministry, Avada Kedavra his several inanimate objects:
[Voldemort] sent another Killing Curse at Dumbledore but missed, instead hitting the security guards desk, which burst into flame. […]
Another jet of green light flew from behind the silver shield. This time it was the one-armed centaur, galloping in front of Dumbledore, that took the blast and shattered into a hundred pieces.
— Order of the Phoenix, chapter 36 (The Only One He Ever Feared)
The Basilisk’s stare is a destructive and lethal piece of magic, but it’s slightly different to Avada Kedavra. As far as we can tell, it’s only lethal when the Basilisk makes eye contact with something; merely looking at something isn’t enough (or Harry would have been dead despite closing his eyes).
In some ways, a camera is a crude version of the human eye. There are a series of lenses that focus the light before it lands on a viewing surface (the back of the eye, or a film). Although they aren’t exactly the same – cameras usually contain mirrors, which is why Colin didn’t die.
So when the basilisk makes “eye contact” with the camera, all that lethal power gets focused at the back of the camera – the film. All that power and magic concentrated on a thin piece of plastic; frankly, the film didn’t stand a chance.
It’s also worth noting that there’s some historical precedent for the basilisk being able to damage objects that can’t technically make eye contact. Quoting from the Wikipedia entry:
Leonardo da Vinci included a basilisk in his Bestiary, saying it is so utterly cruel that when it cannot kill animals by its baleful gaze, it turns upon herbs and plants, and fixing its gaze on them withers them up.
Obviously plants and camera film are a bit different, but it shows that it’s not unheard of for the basilisk stare to be damaging even without eye contact.