Would you use the term "résidence permanente" to refer to the address of stay only or also to a legal permission to be in a foreign country?
For example in Germany the permanent residency address is "dauerhafter Wohnsitz", while the permission to stay is "Niederlassungserlaubnis".
Hypothesis: the permission is maybe "permis de séjour permanent", "adresse de résidence permanente" could be the address I think.
or maybe : titre de séjour, I do not know
"Résidence permanente", literally, is a house where you live in permanently. With a bit of context (e.g. on an administrative form), it can be used to mean the adress of said house. Your hypothesis is correct : the least ambiguate way to say "the adress of that permanent house" would be "adresse de la résidence permanente".
Regarding the legal permission to stay, indeed, "permis de séjour permanent" is fine, or "permis de résidence permanente" also works. If you look at the canadian immigration site for instance, they use "statut de résident permanent" or "carte de résident permanent" to designate the thing that such authorized people have. To ask for it, you file a request called "demande de résidence permanente".
In everyday speech, we use "résidence permanente" to designate the permission, i.e. the status :
Tu as ta résidence permanente ?
Was your request for permanent residency status granted ?
None of this readily translates to France. There is no mandatory registration system like in Germany but different notions of residence for different purposes so that “résidence permanente” is somewhat vague or ambiguous and I would not use it to refer to anything. I am not sure I have heard it either, at least not when referring to France (as opposed to the US or Canada, where permanent residence is something very specific).
What you will find in most legal contexts is simply the word “résident”, which will have a specific meaning depending on how it is used. If you need more details, the appropriate phrase will also depend on the context, for example “résidence principale” (Hauptwohnsitz, as opposed to a vacation home) or “résidence habituelle” (used for civil law or customs purposes).
As far as immigration law is concerned, I don't think France uses the phrase “permanent residence” either. The closest you will find to a Niederlassungserlaubnis is simply called a “carte de résident”. You don't need to add “permanent” because anything less permanent than that will have another name like “carte de séjour”, “visa de long séjour valant titre de séjour”, “récépissé de demande d'asile”, etc. Technically all these, including the carte de résident, are types of titre de séjour.
And outside of legal contexts, I am not sure many people would use the word “résidence”, it sounds very formal. If you are on holidays and want to talk about your usual place of residence, you might say “Mon adresse est […]” or “J'habite à […]”.
Incidentally, Canada does have a permanent residence programme and uses the phrase “statut de résident permanent”.
This is an example of the term in French:
Européen en France : demande de carte de séjour "UE - séjour permanent" Vérifié le 01 juillet 2015 - Direction de l'information légale et administrative (Premier ministre)
[...] : demande de carte de séjour "UE - séjour permanent" Si vous êtes Européen ou Suisse, vous pouvez demander une carte de séjour UE - séjour permanent après 5 ans de séjour légal et ininterrompu en France. Toutefois, ce n'est pas une obligation. Cette règle vous est aussi applicable si vous êtes Croate. Votre carte UE - séjour permanent est renouvelable.
permanent residence = séjour permanent
