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For an hour France were unrecognisable from the team beaten by Italy and Wales in their opening games and scored a brilliant individual try through centre Wesley Fofana to deservedly lead 10-9 at the break.
England struggled to make any impact but the superb goalkicking of Farrell punished the dominant French for their indiscipline and Tuilagai took them clear when he scooped up a loose ball to score 15 minutes into the second half.
A rash of replacements worked in England's favour as they eventually wrestled control in the final quarter and two Toby Flood penalties sealed the win.
England, seeking their first grand slam since 2003, lead the standings with six points from three wins. Wales are second on four after beating Italy earlier on Saturday, with France in last place having lost their first three games.