It's not just France or the lounge. Many (most?) passengers from NCE to other European airports don't go through the passport charade - the one where they wake up the dozing police just for when the British plane arrives or leaves. The French are happy with flights to most European airports being free from document inspection for the most part. It's that Schengen/non-Schengen difference. It does seem that the OP was a victim of intra-EU politics.

Last time I was there, they had separate EU and non-EU arrival lanes with no mention that Swiss should use the EU lane. We were through with our Swiss ID cards in seconds and beat the car rental queue.

IMO the (3rd party) lounge isn't great, anyway.