“Dossier” simply means “file” implying all the documents you need to submit or even simply your “case”. It's not something you get and use everywhere but just whatever you need to put together for a given purpose. A little more context would therefore be needed to give more details.
For example, in the sentence “your dossier doesn't need to be nearly as big as for Paris”, I would interpret that as meaning that landlords won't expect as many guarantees/documents but there is really no canonical list of things you should submit. To a point, it's up to the landlord to decide what they are satisfied with (almost all ask for salary slips, some might want a resume, guarantees from additional people, etc.) Here is a webpage on what landlords can and cannot ask (in French).
I think that all this is the result of the lack of credit rating system and rather restrictive laws on debt recovery and tenant eviction, leaving landlords with a strong need to thoroughly vet potential tenants themselves. In a tight market like Paris, it means they can be very picky and ask for quite a lot of information.