I asked a priest in the US several years ago if the state license could be refused and he claimed he was legally forbidden from marrying anyone without a license.
so not a “marriage” but do a “blessing ceremony”
I doubt if the Lord would mind couples not having a state-issued “license”
If the state doesn't consider it marriage, then he's not performing a state marriage, just a church sacrament.
Priests aren't big on thinking outside the box.
So what to do? Get married in the Church, and then file for an annulment with the state (which will be immediately granted). Unless you get a Church annulment, you are still married in the Church, right? Yep.
We are not too far away from celebrating sacraments in the catacombs, again.