I was taught that the noun "fruit" is non-countable in English.

If so, then what would be its countable counterpart? I am sure there should be one because the need for that is quite practical.

Let's say there is one orange, one apple and one pear on the table.

What would be the right word to refer to all three of them in a countable way, that is, in the way of saying "There are three ... on the table"?

It looks to me like saying

"There are three pieces of fruit on the table"

is rather awkward because both the word "orange", and "apple", and "pear" are all countable. Besides, both orange, apple and pear have their distinctive shapes and edges and are very easily distinguished (unlike, say, a piece of cheese, or a pinch of salt, or a smear of dirt).