"You only have to look at what he did on Alpe d'Huez, for a 21-year-old, that's fantastic", Froome said on Sunday.
"The main thing is we win there and we don't end up racing against each other and Dumoulin wins. The Spanish, fantastic. It just seems to be a French thing", Brailsford said.
He added: "I'm not sure they would like to have seen their (France) football players being spat at (the World Cup) in Russian Federation".
"But it's OK to spit on us and on our staff..."
Team Sky manager Dave Brailsford. "There is a lot in Egan that reminds me of myself when I was younger". She is 21. She's a young girl and she's trying to drive around France and it's intimidating for her. But we're not going to let it distract us.
"I was lucky that it did not affect me too much, I had a bit of tingling in the back of the throat but I used some water to wash it out", said Thomas on the finish line in the spa town of Bagneres-de-Luchon, after keeping his overall lead intact.
Cort Nielsen claimed his first career win at the Tour after staying ahead of Ion Izagirre and Bauke Mollema in a sprint over the final 200 meters.
Froome needs to make time up on the world time trial champion somewhere, though, as he can not sit comfortably in second place with just an 11-second cushion given there is a race against the clock to come on stage 20.
"We get on", he added before breaking out in a grin. We're trying not to react.
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"I'll have to keep thinking about all possible scenarios during the race and, normally, that's one of my strengths".
"The way I see it, I'd rather be in this jersey having the race of my life and getting booed than being 30th and dropped on the first climb and everyone cheering me on". We have a mindset where we don't get distracted by it.
Sky's bid to "remain dignified" was not helped by one of their own over the weekend, when Italian rider Gianni Moscon was disqualified from the race for striking Frenchman Elie Gesbert of Fortuneo-Samsic just 800 metres into Sunday's stage.
But Dumoulin alone is unlikely to panic Sky.
Froome, in particular, has endured more abuse than his Welsh teammate.
"Probably. I don't have an answer to that". "It's certainly not going to calm people down", he said. I'd ask them to call down.
Riders sit after General Director of the Tour de France, France's Christian Prudhomme (Rear L) halted the race, following a farmers' protest who attempted to block the stage's route, during the 16th stage of the 105th edition of the Tour de France cycling race, between Carcassonne and Bagneres-de-Luchon, southwestern France, on July 24, 2018.
"This isn't something new".
Froome has been Sky's undisputed leader since 2013, when he was picked for the Tour de France ahead of 2012 victor Sir Bradley Wiggins. We've been here before and we're experienced at it.