We are so used to Saint-Etienne and their proof marks and have seen so few Paris guns from this time period that I was thinking that perhaps the Paris proof house didn't stamp their guns...which sort of negates the whole procedure.
The date of the barrels is definitely 1880. One of the other numbers either 25230 or 28943 is probably a Bernard number.
Here is a little clearer (enhanced) pic of 25230 number from photo Bill sent.
And Bill, for giggles, I would like clarification on the SNC? after Courier.
Edit, from the linked previous line on Bernard barrels from the Leopold Bernard table by "Wildcattle," 28943 from 1880 would be the Bernard SN: - he was making about 600 barrels a year plus or minus at the time:
24759 1873 Faure Lepage 608
25605 1874 Faure Lepage 647
27268 1877 677
29601 1881 584
30685 1882 Guyot 658