Need complete sentence responses here. Does "yes" reply to "is that necessary"? (Yes, it is necessary in English to begin the sentence with "the woman" not just "woman") Or, does "yes" reply to "can't we just say 'woman eats fish'? (No we can't. Not in English.)
So both previous replies are correct depending on which of the original questions one is replying to.
And either way, it is still "fish". "I eat fish." (not countable) "I caught three fish." (countable). Note that if you name the fish it is countable when it is a food. But some, like "fish" are identical in singular and plural and some are not. One would say "He ate three trout." (not trouts), but "He ate three sardines." (not sardine).
In English "fish" is one of several animal names in which the plural is identical to the singular. e.g. one fish, two fish, one sheep, two sheep, one deer, two deer, one moose, two moose. There is a Dr. Seuss book titled One Fish, Two Fish, Red Fish, Blue Fish. So "fish" is countable, but the plural is the same as the singular.