Clarke, the English Open winner in 1999 and 2000, carded a third-round 68 for a 13-under 203 to join Jacquelin, who finished runner-up last year. The Frenchman stormed to the top with a 65.
Clarke, trying to become the first player to win the English Open title three times, appeared set to lead on his own after a flawless first 16 holes, the highlight coming at the 12th where a 5-iron to inside four seet set up an eagle.
A birdie at the next hole gave him the lead outright at 14-under, but a poor drive and an errant approach shot at the 17th led to a bogey to bring him back into a tie with Jacquelin.
"That was a little bit disappointing because the 17th was the only poor tee shot I had hit all day," said Clarke. "Hopefully, I will be leading on my own tomorrow and not sharing the lead, but there are a lot of very good players out here.
"I have been hitting the ball well for some time now. But I haven't been able to turn it into the scores. I am now starting to do that. Sometimes it clicks and sometimes it doesn't, but as soon as it clicks into place, I am off and running."
Jacquelin's round featured 10 birdies and three bogeys. It was his lowest score on the European Tour this season.
"It was a very strange day because I didn't drive as well as I did on Thursday or Friday. I missed a few fairways, but the putter was very hot," he said. "I think I made 24 putts, which is pretty good putting statistics for me."