Best way from Paris to Heathrow Airport

Flying. Look on Skyscanner for flights from PAR (excluding Beauvais) to Heathrow

Are you doing this on the day of your departing flight from Heathrow?

If your destination actually is Heathrow airport, the easiest option is probably to fly. You choices are Air France or British Airways. But if you are going there to catch a transatlantic flight, it might be a good idea to spend the last night in London.

Always be in the city of a high stakes flight the night before you travel. So much can happen to derail you and travel insurance will often not pay if. you miss an expensive flight due to your own bad planning. Take the Eurostar to London and spent the afternoon and evening and take the train to the airport the next day. That way a late flight, or late train, or cancelled flight or whatever will not lead to disaster.

and if you are going the day before (we have no information), it is much faster to take Eurostar city centre to city centre than to fly, and then calmly make your way to Heathrow the next day...

I agree with taking the Eurostar from Paris to London (2h 30m) the day before your departure. Buy your tickets as far out in advance as possible because the longer you wait the higher the fare.

I have a bad feeling about this. If you're traveling to Heathrow and then catching a flight then the risk of missing the flight out of Heathrow is on your shoulders.

You didn't say what time your flight was out of Heathrow. As suggested above, take the train the day before to London and enjoy your day there. The following morning take the Heathrow Express from Paddington Station to Heathrow for your flight. The terminal you go to will be based on the airline you are flying and where you are flying to. It is a direct train that takes approximately 15 minutes. https://www.heathrowexpress.com/en-GB/timetable/timetable#/
If you aren't interested in seeing London, then your best option is to fly to Heathrow and stay in one of the surrounding airport hotels overnight.