A 20 minute walk from Checkin to a gate at STN? By what method, crawling??
Well start off with trying to get through security when they are busy and not all the security points are being 'personed'. FR do not have any fast track facility. Then find your gate listed. Are you going to be lucky and get away from the FR terminal to one served by the shuttle service? Let's hope there's space on the shuttle train. OK so you have to do the walk of shame to the FR terminal - down, along and up. Is the gate that you were aiming for still the current gate now you've reached the terminal ... and fight your way through to it. I would reckon that 20 mins could easily be clocked up, and that being just trying to get through security without being subject to an additional baggage check or pat down.
And as for 'running' anywhere, as you mentioned, don't forget that there are likely to be bodies and baggage in the way of your intended Olympic sprint, and certainly the Border Agency and Customs folk may take an extra interest in you if you seem to be in too much of a hurry for their taste ... and remember that you will be being watched either electronically or in person during your movements from the arriving aircraft to the departing aircraft.
If the FR flight is late arriving, you might have some luck but I wouldn't count on it. Please let us know how you get on - and genuinely all the very best of luck!