If she can maintain the placings after the final showjumping phase, she will be the first rider to score the double since William Fox-Pitt in 2000.
French has a fence in hand over record four-time Blenheim winner Pippa Funnell on the mare Billy Shannon, with American first-timer Tiana Coudray fourth on Ringwood Magister.
Dressage leader Bettina Hoy is now fifth, having incurred 7.6 time faults on Lanfranco TSF.
Lemington Lett Dance has missed quite a bit of work over the last year and, according to his rider, was in fighting form. "I've never jumped the first five fences so fast in my life - he is a very feisty horse."
DHI Topper, owned by Piggy's father Wally and Michael Underwood, is the horse that so impressed when winning the Olympic Test Event at Greenwich in July.
"I'm really proud of him - it was a beautiful round, as good as he's ever done," said Piggy.
Course-designer Eric Winter is at the Junior European Championships in Portugal, but he will no doubt be delighted to hear that his track has ridden beautifully, producing 65 clear rounds from the 93 starters. There were 79 completions from 93 starters in the cross country.
British Eventing's Chief Executive Mike Etherington-Smith, who is acting course-designer in Winter's absence, said: "There will be a lot of happy horses who have had confidence-giving rounds. The ground was perfect - David Evans's course-building team have done a brilliant job."
There was a surprise elimination for Andrew Nicholson, lying sixth after dressage on Quimbo, when he took the wrong route at an alternative, and William Fox-Pitt, equal 10th on Bay My Hero, incurred 20 penalties at a coffin fence, the Shires Equestrian Wooded Hollow at 9.
Sarah Cohen, fourth after dressage, incurred 20 penalties when Irish Jester took a dislike to David Evans's carved Wooden Tops at fence 12.
There were two casualties. Tom Crisp sustained a broken leg in a fall from Master At Arms at the fourth fence and Lucy Wiegersma has a suspected fractured ankle after a fall from Jumbo's Girl at fence 7.
• In the concurrent CIC***8/9 year old British Championship, William Fox-Pitt maintains his dressage lead going into cross-country on Oslo.
"I certainly am delighted with today. Oslo is a superb horse and a lovely showjumper. Tomorrow is a big course and there is plenty to jump so it should be right to the wire," Fox-Pitt said.
• New Zealand leads the field in the Olympic Team Event after the team section of the CCI *** cross country phase.
Australia, the overnight team leaders after dressage,suffered a setback with Lucinda Fredericks having a fall cross country. With New Zealand having already attained Olympic qualification, this has left Japan out in front - for the one qualifying place - going into the final showjumping phase.
• Crowds were entertained by a select field of seven competitors in the AmTrust Equine High Jump, in which a new Blenheim record was set. Starters were Laura Collett on Jitterbug, Paul Tapner on Tiger Flynn, Nici Wilson on Ucaro, Julie Tew on HHS Foracruise, Austin O'Connor on Zlatan, Alex Hua Tian on Commander and JP Sheffield on DHI Hindle.
The fence started at 1.30m (4'2") and the first competitor out was Alex Hua Tian, but he still managed to clear 1.55m. Laura Collett jumped throughout bareback and cleared 1.80m. This left Austin O'Connor and JP Sheffield left (both shirtless) and they both successfully cleared 1.85 which, is which is where the competition officially finished. As a result the £500 prizemoney was split between them. Both then attempted 1.90m (6'2"), and it was cleared by JP Sheffield's DHI Hindle.
The Riding for the Disabled received a donation of £500 on top of the crowd's contribution.
Pippa Funnell (GB) and Billy Landretti (3rd). © Al Crook
Dan Jocelyn and Zara Phillips walk the course (CIC***8/9yo). © Mike Bain
Alexander Peternell (South Africa) and AP Uprising (7th). © Al Crook
Lucy Jackson (NZ) and Willy Do (24th). © Mike Bain
Bettina Hoy © Al Crook
Takayuki Yumira (Japan) on Hooligan (79th). © Mike Bain
Clarke Johnstone (NZ) and Orient Express (8th). © Al Crook
Jonathan Paget (NZ) and Clifton Razz (17th). © Mike Bain
Bettina Hoy (Germany) and Lanfranco TSF (5th). © Al Crook
Lucy Jackson (NZ) and Willy Do (24th). © Al Crook
Brook Staples (Aust) on Ever So Clever III (45th). © Mike Bain
Jonathan Paget (NZ) and Clifton Razz (17th). © Al Crook
Clarke Johnstone (NZ) and Orient Express (8th).© Mike Bain
Paul Sims (GB) and French Polish (10th). © Al Crook
Some of the army of volunteers it takes to run the Blenheim horse trials. © Mike Bain