When fête is pronounced properly (ie the French pronunciation), it should sound like "fett". However, in BrE at least, it is now pronounced in exactly the same way as "fate". It's wrong but I can't imagine that it will ever change. It's been being pronounced like "fate" for so long and by so many people, I think it's impossible to change it now.
Note that your post should have said "They sound identical to me".
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