The first race in France in a decade and the first at Circuit Paul Ricard since 1990 featured a dramatic opening lap that allowed the Mercedes of Hamilton to clear out as those behind him got caught up in the drama.
"My start was very good, but then I had no place to go", Vettel said. "I enjoyed the race, for me the best French Grand Prix I have ever had".
Vettel returned to the pits for a new front wing while Bottas limped back on three wheels and a rim with the remains of the tyre flailing.
Meanwhile, pole-sitter Hamilton managed to stay out of trouble and maintain his position at the front, where he slowly began to extend his lead. "That's what they said to me at the beginning of the season so should do the same and then of course, Seb shouldn't do anything again and just drive again and learn from this and just go on".
Fernando Alonso, victor of the 24 Hour Le Mans last week, failed to get out of the first qualifying section, which culls the slowest five drivers, along with McLaren partner Stoffel Vandoorne and both Williams cars.
Sebastian Vettel managed to finish fifth after a collision at the first corner saw him damage his vehicle and incur a five-second time penalty.
"You try a little bit too much here and there, you lose the tyre, the auto then it slides and you lose the line". Lauda told Sky F1's Ted Kravitz.
After all the commotion, polesitter Hamilton was leading with Verstappen second, Ricciardo fourth, Vettel 11th and Bottas 13th.
The Finn came in one lap later to rejoin fifth soon after Ricciardo had blasted past an uneven-looking Vettel, who ran wide at Le Beausset.
Verstappen pitted in the 26th lap and came out just ahead of Vettel.
Both cars suffered damage in the collision, Vettel needed a nose change while Bottas picked up a left-rear puncture.
They rejoined from the back of the field to finish fifth and seventh respectively, either side of Kevin Magnussen of Haas, who was sixth.
Formula One driver Lewis Hamilton of Britain (Mercedes) on Saturday won the pole position for Sunday's French Grand Prix. Raikkonen on softer, fresher tyres passed Ricciardo for third on lap 48 but too could not make no further impression.
McLaren's hard weekend also continued with Stoffel Vandoorne 12th and Fernando Alonso sounding increasingly frustrated on the radio and would, in fact, finish as the last classified runner after a late pit-stop to try and set the fastest lap.
Carlos Sainz, Nico Huelkenberg (both Renault) and Charles Leclerc (Sauber) completed the points.
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