Even Paris to Brussels seems to be an issue in November, which could be a bigger issue. From Brussels to Cologne, there are plenty of options using DB Ice trains, but Eurostar is about the only game for Paris/Brussels.
Oddly, I am seeing Paris-Brussels tickets for your time, but requiring a change in Lille, and arriving at Brussels Centraal first. This supports the idea that there is likely maintenance work for Eurostar all along the route.
You can still do it, But booking Paris/Brussels on either Eurostar or Ouigo, Then an Ice train for the Brussels/Cologne route. The number of trains do seem limited, and the trip will take 5-6 hours.
SNCB International also shows the same option, but also suggests Paris to Mannheim/Mannheim to Cologne in 6 hours.