Wouldn’t have thought so - even if arriving at an international airport internal EU-EU transfers will be separated.
Why would they do so in Spain where a French CdS means nothing.
On the way back into France, of course.
I guess this situation must come up from time to time - perhaps the airline can advise if @Shunt really wishes to do it exactly by the book.
Because the residency card of a non national indicates it is ok to travel within Schengen with your passport.
I have flown twice into other EU states to buy cars and checked a while back - first here then confirmed by border control at Carcassonne. Schengen border controls should know this they say, but some might not…!
I should add that both time I flew, it was walk off the aircraft straight though…
It doesn’t though. No more than anyone else entering the Schengen area.
If you fly to Spain and your passport is stamped, meaning that it must be stamped again on re-entry, what happens if you do not fly back but, from a quite innocent need, re-cross at an unguarded border? Who’s going to stamp it then?
The subject has been thrashed quite a bit, already… the thread below started in October 2022 and finished in November 2022… with 95 posts…
So for anyone with concerns… I’d suggest reading (or in some cases re-reading) this link… 
What a palaver, thank you Lord Cameron 
As Stella says we have discussed this previously
Indeed - I don’t think all this has been thought through, it will apply to any citizen of a 3rd nation, not just Brits and is an administrative hassle caused by lack of internal border checks within the Schengen zone.
How do you present yourself to a border guard when there isn’t one at the border?
Hitherto, of course, the problem has largely been ignored as checking of the 90/180 rule was lax but it might rise to bite people once EES and ETIAS kick in.
The most problematic scenario, of course, is not internal travel within Schengen but what happens if, say, a Brit with a French CdS arrives at a Spanish border is logged inbound at that entry point (the French CdS conferring no extra privilege at that point) and then travels into France. As nothing stops the Schengen “clock” they will flag up after 90 days (possibly sooner depending on previous travel) as having overstayed.
As we can see that was exactly the question that kicked off the previous discussion.
That’s the one Stella, my post before yours was rather ruder but I edited before publication , I had said in that thread that the CdS absolved us from needing a visa in other Schengen countries but was then told that no-one needs one anymore. So not even that tiny privilege for being long term law abiding residents. 
Your French CdS only stops the 90/180 day clock ticking in France - you might not need a visa to travel elsewhere in Schengen (as we did, at least, manage to retain visa waver agreements post Brexit, although there was a period where even that looked dodgy IIRC).
But it’s a general problem, not just for Brits.
The answer, clearly, would be a Schengen CdS - but I can’t see that being agreed.
Never seen anyone at La Jonquera and we cross for shopping quite often, taking my passport with me just in case though if a drugs check operation shuts the road.
I posted elsewhere that I met a UK citizen who lived in a German / polish border town - he lives on the polish side of the river and works on the German side.
He sometimes flies into German airports from the UK after visiting and I asked him how it works for him re passport stamping. He said he shows his Polish residence card and they don’t stamp his passport.
ps here’s another previous thread on the subject -
Me too. Several trips to a dentist in VLC - just stroll out, no p/port checks.
No border checks by road going into ES. Only once stopped at the FR duanes returning in a car on FR plates. I think they spotted RHD and decided to have a gander. And again, some many kms up the road, a checkpoint at a rond point. Passport and CdS checked but no stamps ever.
Same at Ouistreham and Dieppe - straight off, no checks.
OK. If you say so. Let us leave it at that. I am just telling you what the border chappies tell me. But like so many other things that I have asked the authority concerned and relayed here, no doubt they are wrong. 
‘It might not be’ because rules seem to be inconsistently applied. I got no stamp in Lanzarote or Portugal earlier this year, flying from UK for first trip and France for the second. I would have thought I would get a stamp even when showing residency card but clearly this isn’t always the case. So my question was for those who ‘know’ the answer, so that I have a definitive answer.
Err…how? There’s always a passport check on arrival at Ouistreham, & adding the CdS always gets you a cheery smile.
If by “the authority concerned” you mean border guards I wouldn’t regard them as an authoritative source on the law - we’ve heard numerous examples of people with a valid CdS getting passports stamped on entry to France which is wrong.
If you have a reference to actual EU/Schengen law which says that a non-EU citizen holding a residence permit in one EU member nation can enter another Schengen member using just their residence card then please share it.
You do raise an important point though - which is that border guards aren’t always as informed about the law as one might like, especially where the law is new, or newly being applied.
TBH I would not envisage the slightest problem if travelling from one EU member to another, if you always exit and enter through your host nation, using your residence permit to demonstrate that you have right of entry/abode.
Where it might be a problem is entering via an EU nation which is not your host nation.
In due course I expect this will all be worked out, in the meantime until EES/ETIAS is up and running it probably won’t be an issue in practice.
Edited to acknowledge @Adam1’s point below.
Again. Forums.
I never said anything about overriding the 90 day rule.
Now, did I?
OK, fair enough.
You did say “Because the residency card of a non national indicates it is ok to travel within Schengen with your passport”
The thing is that having a residency card for one state does the square root of nothing for your ability to enter another member state. If your country of nationality has a visa waver scheme you can enter subject to the 90/180 rule with no formality. If you need a visa to enter then you *still* need a visa to enter, whether or not you have residence in some other EU nation.
Fortunately the UK has visa waiver agreements with all of the Schengen nations.
Once more for clarity - if resident in one EU member state entry to others depends on the normal Schengen rules as determined by your passport, your residence permit makes no difference at all, it does not confer extra privilege.
Whatever the last border guard you met says.
Yes. True. By Brit Ferries check-in staff but not by douanes. I s’pose their records are available to douanes and there’s probably NPR cameras clocking every vehicle. However, nothing coming in …