What do you call this part of the sentence that describes a quotation in a dialog?

Question

In this dumb example:

— I can hardly find a good example, he said.
— I know, she answered, I can hardly find one too.

What do you call the bold parts of the sentences, which describe how the character is speaking?

I've found many questions/answers about the use of a comma before a quotation, nothing related to the name of the part of the sentence introduced by a comma after a quotation, especially inside a dialog.

If I translate the french word for this in english, it should be a parenthetical element. But in all I've read so far, parenthetical elements never appear in dialogs (I mean in the construction of the dialog, since a character can pronounce a sentence with a parenthetical element, that's not the question).

EDIT: The french word is incise. Sorry I forgot...

Answer 1

I believe this is called the reporting clause

Reported speech: reporting and reported clauses
Speech reports consist of two parts: the reporting clause and the reported clause. The reporting clause includes a verb such as say, tell, ask, reply, shout, usually in the past simple, and the reported clause includes what the original speaker said.