Other countries’ residency cards

I have residency permission for Sweden. Will I be required to complete EES registration/Etias authorisation when entering France from a non-EU country such as the UK or will my Swedish residency suffice? 

Nobody who lives in a Schengen country, with a long-stay visa and/or residency card should be required to be registered in EES or to obtain Etias authorisation. 

The fact of having long-stay residency in an EU country means that you have the right to come into the Schengen area due to this residency status (so Etias permission is irrelevant), and this includes the right to transit through other member states on the way to the one where you live.

Long-stay visa/residency card holders in an EU state are in fact meant to respect the rule of 90/180 days with regard to visiting other Schengen states, but it is not the aim of the EES to monitor this but rather, among other points, to check there is no ‘overstaying’ by short-stay visitors to the area. 

You should, however, make sure to have your residency card with you as proof of your status.