I'll take a shot..
If you need to be in Paris by 2000 then that equates to 1900 British time. I would assume you can just make it by taking the 1622 Eurostar.
Working back from a 1622 departure, you'll need to check in at St P 1552.
Including waiting and ticket time I would allow one hour for Heathrow Express to Paddington and then underground or taxi to St P. Taxi direct from Heathrow to St P would be about the same.
All this means that you need to be looking for a Heathrow Express ticket at Heathrow around 1445, which is about 80 mins after your scheduled landing.
Within that 80 mins is all your contingency so I'd say the 1622 Eurostar is the earliest I'd want to be taking.