Do you have the fire district data as GIS information -- say a shapefile or GeoJSON? If so, there are methods for identifying the census geographies contained within or intersected by the geometry of the fire district. I (or other folks on this list) could probably give a few pointers on how to do that, but it would be kind of involved and not for all tastes.
Alternatively, you could just find a map of Census tracts and build a list. I think 1200 households is close to the median tract, so it probably wouldn't be a long list. You could find a tract in the district on our Census Reporter project by entering a known street address in the district at
censusreporter.org/.../ If you then click on the Census Tract which contains that address, you'd see a profile page for a single tract. Using the map at the top of the page, you could mouse over and/or click through to other tracts in the Fire District, noting the URLs of each. There's a coded part of each URL that begins with "14000US" (for tracts). the part after the "US" can be broken down into State FIPS code (first two digits), County FIPS code (digits 3-5), and Tract ID (digits 6-11, with an implicit decimal point between digits 9-10)
Hope that helps.