FUSE spectra of the four brightest H II regions in M 33 show absorption by interstellar gas in the Galaxy and in M 33. On three lines of sight molecular hydrogen in M 33 is detected. This is the first measurement of diffuse H_2 in absorption in a Local Group galaxy other than the Magellanic Clouds. A quantitative analysis is difficult because of the low signal to noise ratio and the systematic effects produced by having multiple objects in the FUSE aperture. We use the M 33 FUSE data to demonstrate in a more general manner the complexity of interpreting interstellar absorption line spectra towards multi-object background sources. We derive H_2 column densities of approximately 10^16 to 10^17 cm^{-2} along 3 sight lines (NGC 588, NGC 592, NGC 595). Because of the systematic effects, these values most likely represent upper limits and the non-detection of H_2 towards NGC 604 does not exclude the existence of significant amounts of molecular gas along this sight line.
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