I'm pretty sure about this

I don't know of any similar process in the English-speaking world.

The basic idea is a "huissier" identifies the person, makes a formal declaration and writes down an official report of whatever the person says (if anything).
This report can then be used in evidence.
The main purpose is to force the person in question to take a definite stance on an issue or to prove that he has been informed of something. Failure to answer therefore becomes, in itself, admissible in evidence.

Unfortunately I don't have a direct translation. I would include call it a "served declaration and observed response" and put the French in brackets.

Sources: multiple descriptions on the internet, often with reference to Art 800 Civil Code (heir summoned to disclose where inherited property is) or Art 1479 Civil Code (debts between spouses bearing interest only from the date of "sommation").
Interestingly no actual appearance of the word "interpellative" in the French Civil Code, Civil Procedure Code or Commercial Code. It seems to be something that has arisen in practice more than by law - but the amendment to Art 800 Civil Code adding "sommation" (previously "mise en demeure") is recent (2007).

Finally - yes documents may be requested by a "sommation interpellative" but the effect of failing to produce the requested documents is merely the effect that the law provides for in such cases: the "sommation interpellative" is used to prove that the demand has been made, rather than bearing any kind of forceful weight in itself, as a subpoena does.