From the translation of the Hadopi law (provided here: http://www.laquadrature.net/wiki/HADOPI_full_translation
"Art. L. 331-27. - When it is held that the subscriber has failed to recognize the obligation defined in article L 336-3 during the year following the reception of an injunction sent by the committee for protection of rights and accompanied by a receipted letter or any other method needed to establish proof of the date that the injunction was sent and that when the subscriber received it, the committee may, after a hearing, pronounce, as a result of the gravity of the violations and the use of access, one of the following sanctions:
"1 The suspension of access to service for a duration of two months to one year accompanied by making it impossible for the subscriber to subscribe during that period to another contract giving access to a public on line communication service with any operator;
"2 A warning to take, within a time it determines, measures to prevent the renewal of the accused violation, particularly a method of security found on the list defined in the second paragraph of article L. 331-32, and to inform the High Authority, if necessary under duress.
I heard somewhere that Item 2 hints at the possibility of putting some "Approved Software" on the subscribers' PC(s) which will monitor activity and stop the PC(s) infringing copyright. No doubt it would only run on Windows. However it is very hard to find any real information about this. The referenced article 331-32 looks like it might have some meat in it but alas no...
"Art. L. 331-32. - After consultating the creators of means of security intended to prevent illicit use of access to a public on line communication service, entities whose activity is to offer access to such a service, as well as companies governed by title II of this book and duly constituted professional societies, the High Authority makes public the functionally pertinent specifications presented by these means considered, in its view, as exonerating from responsibility the owners of such access under the conditions of article L. 336-3.
"In the course of a procedure of certified evaluation of their conformity to the specifications set forth in the first paragraph and their effectiveness, the High Authority establishes a list characterizing the methods of security whose use exonerates the owner of access of his responsibility with respect to article L. 336-3. This characterization is periodically reviewed.
"A decree of the Council of State specifies the evaluation procedure to characterize these methods of security.
Maybe the referenced Article L.336-3 will explain...
"Art. L. 336-3. - The owner of access to online public communication services has an obligation to watch that this access is not being used for purposes of reproduction, representation, making available or communication to the public of works or objects protected by right of authorship or a related right without permission of copyright holders when it is required as stated in books I and II.
"No sanction can be taken against the owner of the access in the following cases:
"1 If the owner of the access has secured his access through one of the means on the list mentioned in the second paragraph of article L. 331-32 ;
"2 If the rights infringement referred to in the first paragraph of this article is committed by a person who fraudulently used the access to online public communication service;
"3 In case of force majeure.
"The breaching of the obligation defined in the first paragraph by an access owner hasn't the effect of involving his penal reponsibility.
... and maybe not.
I also understand that the line remains in service and the subscriber is billed for it (unless she chooses to pay to terminate the connection) but only commercially provided protocols are enabled (telephone and TV). See this post for the wording of the law. http://yro.slashdot.org/comments.pl?sid=2462320&cid=37623774