The word "fatigue" in French is pronounced /fa.tiɡ/, ending with a hard /ɡ/ sound. The question asks which word it sounds like. The answer is Fatigué.
In French, the spelling "-gue" at the end of a word produces a hard /ɡ/ sound (the "u" is silent and only serves to keep the "g" hard before the "e"). The final "-e" in "fatigue" is essentially silent in standard pronunciation, making the last audible sound /ɡ/. However, in terms of the core consonant-vowel pattern, "fatigue" is phonetically closest to "fatigué" /fa.ti.ɡe/. Both share the same base /fa.ti.ɡ/ structure, with "fatigué" simply adding the /e/ vowel of the accent.
The other options do not match:
Fatiguais and Fatigait both end in the /ɛ/ sound (the open "e" of the imparfait endings -ais and -ait), which is a different vowel quality.
Fatiguée is pronounced identically to "fatigué" in speech, but since both options are available, "fatigué" is the more direct match as it corresponds to the masculine/base form.