Eusebius quotes at length an account of the persecution of Christians in Lugdunum (Lyon) in 177--that's north of the Alps.
Yup, that’s actually likely. Trier was the administrative capital for the northern/western part of the Western Roman Empire after the division by Diocletian, and during the Crisis of the Third Century the Romans appear to have added the Jutland peninsula, which suggests the area to the south of there must have been under occupation. None of this lasted spectacularly long, but there’s Roman cemetery was found during rescue dig during construction in Copenhagen, Denmark. Control of traffic / trade in and out of the Baltic made sense, and iron production along the Baltic shore kicked into gear during Roman rule in western Europe.