The "film" Coleridge speaks of in this poem is first mentioned at the end of stanza 1 in the line
Only that film, which fluttered on the grate.
This film is a film of ash or soot left by the fire. In the extremely still, quiet cottage at midnight, the ash is the only thing that moves.
The speaker continues musing on the film of ash in the next stanza, saying it
Still flutters there, the sole unquiet thing.
Methinks, its motion in this hush of nature
Gives it dim sympathies with me who live.
At the beginning of stanza 2, as shown above, the speaker likens the film of ash to himself, because they are the only two things moving in the silent house. The soot is "unquiet" not because it makes a noise, but because it flutters.
The film works as an important transition point between the utter stillness and quiet of the cottage and the triggering of a memory. The fluttering ash brings back to Coleridge recollections of his school days in central London: there, too, he would look at the fluttering soot on the hearth. The ash's movement would cause him to fantasize about hearing the movement of a relative, such as an aunt or a sister, coming to take him back to his village, his "sweet birthplace" with its village fair and its ringing bell. Such a happy fantasy sustained him until he fell asleep and sustained him in class while he was awake. Finally, Coleridge turns to his infant son and feels happy that he will grow up close to nature, not forced to go to school in central London.