Follow up to this question. When is it illegal to threaten someone with taking them to court?
Threat of lawsuit can't be illegal
It is a basis of functioning legal systems, that if you have a case, you can sue. However, nothing in any such legal system requires them to sue. Instead, offering a resolution out of court - like arbitration or offering to relinquish a claim for payment - is legal. Adding pressure by saying "This is my offer, otherwise I sue" is not extortion, because after the suit is filed, it is with the courts. Should the claimant file a frivolous lawsuit, then the court will deal with it - dismissing the case and sanctioning the claimant and their lawyer.
See also these questions:
When you make “unwarranted demands with menaces”
NSW Crimes Act 1900 s249K.
"unwarranted" unless the person believes that he or she has reasonable grounds for making the demand and reasonably believes that the use of the menaces is a proper means of reinforcing the demand.
(a) an express or implied threat of any action detrimental or unpleasant to another person, and
(b) a general threat of detrimental or unpleasant action that is implied because the person making the unwarranted demand holds a public office.
A threat of a lawsuit is a “menace”. If you do not believe that your lawsuit can survive summary dismissal then it is “unwarranted”.
In france, such threats can be extortion, depending on the surrounding circumstances.
Extortion is defined by article 312-1 du Code Pénal:
L'extorsion est le fait d'obtenir par violence, menace de violences ou contrainte soit une signature, un engagement ou une renonciation, soit la révélation d'un secret, soit la remise de fonds, de valeurs ou d'un bien quelconque.
It is extortion to obtain by violence, threat of violence, or constraint; either a signature, a commitment or renunciation; or the disclosure of a secret; or the gift of money or goods.
"Constraint" is of course a rather vague word and there is a decent amount of case law on the subject. In particular, it can be applied by making threats to do entirely legal things. The case in point is Cour de cassation, criminelle, Chambre criminelle, 3 novembre 2016, 15-83.892.
In that case, a student threw something at a teacher and injured him. The teacher went to the parents' house and threatened to press charges as well as ask the high school to kick out the child. The teacher then came back shortly thereafter with a settlement document, which the parents signed, agreeing to pay €7500.
Sidenote: "press charges" is in French "porter plainte". With that fact pattern (violence causing personal injury), you would seek court action via a police criminal complaint to which you add yourself as "partie civile". The court then rules on both the criminal case and the associated tort.
The teacher was condemned for extortion for the way he made the parents sign the document (as well as how he pursued them thereafter but let’s leave that aside). He appealed to the Cour de Cassation, arguing among other things that
(...) la contrainte propre à caractériser un fait d'extorsion portant sur un engagement s'entend d'agissements préalables de l'auteur tendant, par leur illicéité et leur gravité, à forcer directement la volonté du signataire qui, autrement, ne se serait pas engagé ; que la contrainte, au sens de l'article 312-1 du code pénal ne peut résulter du déséquilibre prétendu de l'engagement ni du statut respectif des signataires, ni de l'insistance prêtée au prévenu dans la recherche d'une réparation amiable, ni enfin dans le sentiment exprimé a posteriori par le plaignant de s'être senti « obligé » ou « contraint »
constraint means previous actions that are illegal and grave, which force the victim to grant a signature they would otherwise have refused; constraint under article 312-1 cannot be the result of a claimed imbalance in the terms agreed, nor of pushiness by the one who proposes a settlement, nor of an after-the-fact feeling of "I had to do it" by the appellee
My emphasis. The translation is a bit loose, in particular "illéicité" is an ambiguous word; it usually means "unlawfulness", but could also be a stronger version of "immorality". That ambiguity might have been intentional from whoever drafted the appeal.
The Cour de Cassation rejected that argument. While the teacher was allowed to press resolution by either police or administrative action, he threatened those to build up pressure on the parents, and the surrounding circumstances meant that it constituted constraint.
That does not mean that one cannot make threats to induce settlements in France. Imagine a bar owner telling unruly customers to pay their drinks or else he will call the police - that would not be extortion. It just means that all circumstances have to be considered, and the exact content of the threats does not suffice to make them legal.