Portugal beat Switzerland 2-0 in Lisbon thanks to a Johan Djourou own goal and an Andre Silva strike.
France needed goals from Griezmann and Olivier Giroud in a hard-fought 2-1 win over Belarus at the Stade de France.
After a stuttering campaign, France’s achievement in beating Bulgaria and Belarus in their final two qualifiers means they avoid the playoffs having had to go through that route for the last two finals.
“We have had a difficult route and tonight wasn’t easy either but we’ve achieved our aim,” coach Didier Deschamps said.
“We are happy, even if qualifying is logical given the quality of the players I have.”
– French relief –
Giroud said he was delighted to have avoided the tension of the playoffs.
“We’re all relieved tonight to have ended the campaign with automatic qualification,” the Arsenal forward said.
“We chased this game and it wasn’t easy because they were strong and efficient in attack until the final whistle and we had to roll up our sleeves.”
The Dutch, World Cup finalists in South Africa in 2010 and semi-finalists four years later, bowed to the inevitable as they failed to achieve the unlikely 7-0 scoreline over Sweden they needed to salvage a wretched qualifying effort.
Arjen Robben scored twice in a 2-0 win over the Swedes in Amsterdam and said afterwards he was retiring from international football.
“I will always remember the 2010 World Cup and 2014. Those are my best memories. During those two competitions we formed a real team,” the 33-year-old Robben said.
– Playoff tension –
In Lisbon, Portugal navigated a potentially fraught final fixture with Switzerland, who become one of the eight European nations who must fight through the playoffs for a spot in Russia.
The others are Italy, Denmark, Croatia, Sweden, Northern Ireland, Greece and the Republic of Ireland.
The Swiss can consider themselves unlucky after winning all nine previous qualifiers but must now overcome a two-legged play-off in November to earn a fourth straight World Cup appearance.
Ronaldo, who was injured for the opening qualifying defeat in Basel, returned to the Portuguese line-up after coming off the bench to notch the opening goal in a lacklustre 2-0 win in Andorra on Saturday.
US pop star Madonna was among the crowd at the Estadio da Luz which erupted when Djourou inadvertently bundled in a dangerous cross from Eliseu four minutes before the break under heavy pressure from Joao Mario.
Manchester City midfielder Bernardo Silva then exchanged passes with former Monaco team-mate Joao Moutinho, threading through the return pass for an unmarked Andre Silva to poke in at the far post.
Greece locked up second place behind Belgium in Group H courtesy of a 4-0 stroll against Gibraltar.
In Paris, Deschamps paired Atletico Madrid striker Griezmann with Giroud’s aerial threat, and Griezmann eased nerves in the 27th minute as he opened the scoring with a confident low finish from Blaise Matuidi’s deft pass.
Six minutes later, Griezmann intercepted a weak pass out of the Belarus defence and fed Giroud, who shrugged off two defenders to bundle in his 28th international goal.
But the French defence was caught napping, allowing Belarus to reduce the gap when the lively Anton Saroka swept past Hugo Lloris a minute before half-time.
Saroka gave France another jolt when he shot just wide in the 64th minute, but he was narrowly offside.
Deschamps brought on Paris Saint-Germain starlet Kylian Mbappe in the second half to inject pace and fresh ideas, but with the seconds ticking down to the final whistle, it was Saroka again who slid a shot just wide from close range.