So PAR (and other French cities) have joined the fray. Only *A so far.
Fares from a little over €1230 to most US / Canada destinations. I think the highlight is to HNL about €1400.
Example
This is the cheapest fare (I think) at this point in time from a Western EU city to North America by the ‘major’ carriers.
All these fares in this thread I think are available till 30 April 20. Although one suspects they will be more coming.