Froome recovered and defended himself on the summit finish below Mont Blanc. He crossed the line with blood showing through his yellow leader's jersey, but maintained the famous top by 4-11 over stage winner Romain Bardet (Ag2r La Mondiale).
"Today is that kind of day that I'm grateful to have a four-minute advantage, to fall back on," Froome said. "It was great to have all the team around me, Wout Poels in particular. All the guys. It was a great team effort. It feels good to be one day closer to Paris.
"Today shows exactly why [anything can happen in the Tour]. I'm really grateful to see nothing seriously injured, it could've gone either way there. There’s never a dull day in the Tour."
Froome defended himself from attacks by Richie Porte (BMC Racing) and Fabio Aru (Astana). Frenchman Bardet rode clear at the base of the climb while team Astana had control. He won by 36 seconds over Froome, who finished side by side with Dutch helper Wout Poels.
Colombian Nairo Quintana (Movistar) gained 10 seconds, Aru eight. Froome, however, leads the overall over Bardet, who moved from fourth to second overall. Quintana is at 4-27 minutes in third.
Froome slid after many others fell, including Porte, Bauke Mollema (Trek-Segafredo) – who was second overall this morning – Tom Dumoulin (Giant-Alpecin) and Pierre Rolland (Cannondale). A white painted line on a right curve at 11.2 kilometres from the finish to race appeared to cause the accident.
"It's ironic really, I was trying I was trying to stay up front and out of trouble, just hit one of the white lines and lost my wheel," Froome said.
"I'm OK. I'm lucky, nothing seriously injured. I just lost a little skin and banged my knee a bit."
Geraint Thomas immediately stopped and passed Froome his bike. Froome rode it up the Bettex climb and with the help of team-mates Sergio Henao, Mikel Landa and then Poels, over the finish line 9.8 kilometres later.
"I knew the car was a ways back and my bike, I could see it wasn't rideable," Froome added. "Thanks to Geraint for his bike! I rode that to the finish, it was all right."
Vincenzo Nibali (Astana) fell behind Froome. He told Cycling Weekly that it was not the fault of Sky’s leader, but that “everyone seemed to be crashing today”.
The 20th stage tomorrow covers 146.5 kilometres and finishes with the Joux Plane climb and descent to Morzine. Froome's condition remains unknown.
"Certainly, it's going to be hard, really hard. I'm sure I'll be stiff and sore after today," added Froome. "Hopefully, I'm going to rely on my team-mates and just have one last push to get through tomorrow's stage."
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