The result sees Ireland claim the trophy with one game to spare, setting up a showdown with England at Twickenham next weekend which could see the Irish pull off a Grand Slam for only the third time in their history.
Ireland's 28-8 victory over Scotland earlier in the day had left England needing four tries and a win in Paris to claim the bonus point and take the championship down to the final day, but in the end they slumped to a second consecutive defeat for the first time under Eddie Jones to hand Ireland the title.
The two sides exchanged penalties in a tight first half during which neither were able to show their best attacking rugby, going into the break locked at 9-9.
The hosts missed a good opportunity to drive home their advantage when they squandered a four-on-two overlap, but another penalty did enable them to extend their lead to 10 points after Watson was reintroduced to the game.
It was England's ill-discipline which cost them again - conceding 16 penalties throughout the match - but they did give themselves hope of at least winning on the day when Jonny May crossed over for their first try after good work from Elliot Daly.
Stand-in captain Owen Farrell slotted the conversion through from the touchline, but once again a penalty undid much of their hard work as France were able to nudge themselves six points ahead in the closing stages.
At that stage it was clear that the title was already beyond England's grasp, but they did push forward in search of a try which would help them to victory in Paris, only for a knock-on virtually on the French line to bring an end to the match.
The result sees the defending two-time champions surrender their crown to Ireland ahead of their showdown with the new title-holders at Twickenham next weekend, whereas France will end their campaign in Wales.