The contest between the two ex-premiers has taken a bitter turn, leading more than 200 Republicans lawmakers to publish a pro-Fillon column urging a more civilised discussion.
Whoever wins the primary is widely tipped to become next president after elections in April and May against a resurgent far-right National Front (FN) and weakened Socialist Party.
A poll published on 23 November showed François Fillon would win 65 percent of votes in the final primary vote on 27 November against 35 percent for the more centrist Juppé.
"I'm holding the line and am keeping a cool head, but by the look of things there's powerful momentum that has been unleashed," Fillon, a social conservative with bold economic reform plans, told Le Figaro newspaper.
Polls for the first round, however, failed to forecast Fillon as the overwhelming winner as he surged past Juppé and former president Nicolas Sarkozy, who was knocked out.