As mentioned on https://www.service-public.fr/particuliers/vosdroits/F31267, it is legal for the owner to require a garantor (a caution), notice that it is not mandatory.
La présentation d'une caution n'est pas une obligation légale.
Toutefois, un bailleur peut exiger la présence d'une caution pour
louer son logement. En pratique, c'est souvent le cas y compris si
vous êtes candidat à un logement social.
It is also explicitly mentioned that the caution cannot be rejected because they are not French.
le propriétaire ne peut pas refuser la caution au seul motif que cette
personne ne possède pas la nationalité française.
There is also a template letter for the caution.
It is explicitly mentioned that the documents that the caution must provide should be redacted or translated into French and that monetary values should be in euros. (See https://www.service-public.fr/particuliers/vosdroits/F1169, Documents demandés à la caution tab).
il est possible de fournir une copie des documents originaux. Les
documents doivent être rédigés ou traduits en français, et les
montants inscrits convertis en euros. Toutefois, le propriétaire a le
droit d'exiger la présentation de l'original des documents.
So from the legal point, there's no obstacle to Swiss parents being caution for their daughter in France.
Now, let's face some issues:
Paris area housing market is notoriously very difficult, even for natives. Given ten candidates with similar credentials, the agency or owner will probably go the easy path (ie french caution with french credentials). Expect high prices.
The standard contract for furnished apartment in France is one year long. Looking for a six months rent adds to the difficulty. You are in a zone between short-term and long-term.
Paris has begun to enforce a 120 day a year maximum duration for private owners renting their apartments thru airbnb or similar platforms. That might limit the opportunity to find a six months offer on such platforms.
Networking: see what help or advice the place where your friend is doing her internship can provide. Maybe some people working there do have a room to rent or a sub-location (known as colocation in French) to share ?
About networking : many corporations or school in France do have some sort of informal classified ads in place. That might be a panel close to the coffee machine where one can pin an ad or an electronic mailing list, .... I would suggest to get in touch with her contact at the place of internship and ask whether such a system actually exists and if her contact could publish her request.
As for the guarantee agency you mention, I cannot give any feedback. It seems legit, and they mention that you only pay their fee when the renting contract is signed, so the risk seems low.
Use agencies dedicated to this type of mid duration rent. They are usually used by high profile customers (diplomatic corp, corporations) so the cost will accordingly be high, but you can nevertheless check what their offers are.
If the internship is part of a university course and your friend has a student status, see whether there might be offers from students bodies like http://www.crous-paris.fr/logements/nos-logements/. Chances are low because it is in high demand, but there might be useful advice from this kind of institution.