This is not quite the whole picture. While it is true that the 'm' in 'faim' is not sounded as a classic 'm', it does have a determining effect on the pronunciation of the word.
Consider the following words: 'fait' & 'faim'. The 't' in 'fait' is truly silent and the word is pronounced¿[fɛ] If the 'm' in 'faim' were truly silent then both words would sound identical. In fact the 'm' in 'faim' causes a nasalisation of the sound and thus 'faim' is pronounced [fɛ̃].
Hope this helps.
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