Ah yes, I'm old enough to remember travelling to France in the early 70s but anyhow thanks for the reminder about how it worked.. of course don't forget there wasn't the Schengen agreement back then either so the down side of the good old days was that in theory at least passports needed to be checked at every European Border....nowadays for the locals it's definitely more efficient, especially if you live very near an internal Border like we do.
OTOH yes it's extra faff for any non-EU passport holder entering the Schengen zone at any external frontier, not just a French one, who lacks either a Schengen Visa or EU residency permit but the clock isn't going to be wound back to the 70s just because Dover can't cope.
If the French choose to be bolshy and make things difficult for British travellers by striking, rioting, working to rule, operating at minimal staffing levels especially at busy periods, that's up to them.
Glad you said "if" there because with regard to Dover and last weekend - there were no national days of action with regard to the pension reforms over the period - last national day of action here was last Tuesday, FWIW next one is this coming Thursday so it was all quiet on the manifestation/protest/riot around and during last weekend. There was no PAF (i.e. Border police) work to rule either....
Looks like a problem for Dover to "own" and sort out.