for the posterity of SEO, i will say that as someone who plies the NYC-Paris route a lot (a lot a lot), i have observed that the route was generally affordable around Thanksgiving -- if you can even afford to leave on Tuesday rather than Wednesday for example (flights being a night in the Eastward direction, a Thanskgiving traveller who's not adding extra time off from work would fly Wednesday evening).

My entirely anecdotal perception is that Americans do of course travel a lot during Thanksgiving but generally head out to their family elsewhere in the US. You also have American expats heading to America from their international home-bases to celebrate Thanksgiving for their family, but this has an impact on Intl-US-Intl routes, and not US-Paris-US flights

I always tell my American friends that if they are in a position to travel internationally for Thanksgiving and despite the sense that everyone is travelling that week, they won't find egregious prices for their international travel.