In French, and also in the English usage of this phrase, the spelling is 'Bon appetit', without an 'e'. The only difference it that the correct French spelling is with an accent - appétit ‎- while English doesn't tend to use the accent.

English-speaking people often use French phrases in certain situations where there is no exact equivalent in English. As Derrick points out, we do say 'Enjoy your meal', but we also sometimes say 'Bon appetit'. Like 'Bon voyage', it's a French phrase commonly used within the English language.

'Bon appetite' is 'franglais' - a mixture of the two languages. It's either written by an English speaker who doesn't know the correct spelling, or an error generated by an English spell check that didn't recognise 'appétit'.

what hapen fren?