On the qualification for teacher-researcher/enseignant-chercheur (MCF) positions in France and its recent abolition - what exactly does the law say?
Since there seems to be some uncertainty in the other answer / comment thread, I will offer my point of view. (I'm a MCF in a French university.) If you just want the answer, skip to the section that starts by It depends below.
You are misreading the information available. Qualification was removed for PR jobs. It remains mandatory in most cases to be a candidate for MCF jobs. The reply by Galaxie (which you should take as authoritative: Galaxie is managed by the HR department of the ministry of higher education and research, and they are the ones who are going to process your application) is pretty clear about that: if you are not already a titular MCF, then you need the qualification to be a candidate for MCF positions. This is also what is written in your links. I will provide translations in case you are not a French speaker:

(link1) Toujours est-il que la qualification aux fonctions de professeur des Universités est supprimée. =&gt; Nevertheless, the qualification for the assignment of professor was removed.


(link2) L’article 5 de la LPR supprime la qualification par le CNU pour les maîtres de conférences (MCF) qui veulent accéder au corps de professeur des universités (PR). =&gt; Article 5 of the LPR [Law of (budgetary) Programmation of Research] removes qualification by the CNU for MCFs who want to reach the ranks of professors.

And since nothing beats actually looking at the actual law, here it is on the French Republic's official legal website: https://www.legifrance.gouv.fr/jorf/article_jo/JORFARTI000042738037

Article 5
Le code de l'éducation est ainsi modifié :
1° Au premier alinéa de l'article L. 952-6, après le mot : « particuliers », sont insérés les mots : «, et sauf lorsque le candidat est maître de conférences titulaire » ;

In short, persons who are already titular MCFs are not required to pass the qualification anymore. Moreover, if you read the rest of the article of law, some universities may ask to receive the permission to hire persons for any job (MCF or PR) without the qualification. But every university will have its own policy on this.
So to answer your question:

can a foreigner apply to the MCF positions now without having the qualification?

It depends:

If you are already a titular MCF, then yes;
If you are applying to a job in a university that has asked and has received the authorization to hire MCFs that have not received the qualification, then yes;
In other cases, that would be a no.

The nationality of the applicant is in principle irrelevant. French nationals and foreigners alike are bound by the same laws for French academic jobs.
Note that to my knowledge, since the law is very recent, no university has yet asked for an exemption from the qualification procedure (since this is a hot topic, I would have heard about it, at least if it were for jobs in my field).
Given the possible discrepancies that will appear between the universities' policies regarding the exemption, your best bet is to get the qualification. Note that the procedure starts very early, in October of the year preceding job applications, so be proactive about it! Don't wait at the last minute, if you miss the deadline you have to wait a whole year.
Finally, note that the law about the exemption (case 2 above) is marked as experimental and the experiment will end in 2025. At that time, there will again be a vote on the law and it will either be maintained or rescinded.
Welcome to French academia, where the rules change all the time, no one's really sure of what's forbidden or allowed, and an error can easily cost you opportunities. Enjoy your stay :)