https://en.wikipedia.org/wiki/Russo-Georgian_War#Relations_between_Georgia_and_the_West

During the NATO summit in Bucharest in April 2008, American president George W. Bush campaigned for offering a Membership Action Plan (MAP) to Georgia and Ukraine. However, Germany and France said that offering a MAP to Ukraine and Georgia would be “an unnecessary offence” for Russia.[99] NATO stated that Ukraine and Georgia would be admitted in the alliance and pledged to review the requests for MAP in December 2008.[100] Russian President Vladimir Putin was in Bucharest during the summit. At the conclusion of the summit on 4 April, Putin said that NATO’s enlargement towards Russia “would be taken in Russia as a direct threat to the security of our country”.[101] Following the Bucharest summit, Russian hostility increased and Russia started to actively prepare for the invasion of Georgia.[102] The Chief of the General Staff of the Russian Armed Forces Yuri Baluyevsky said on 11 April that Russia would carry out “steps of a different nature” in addition to military action if Ukraine and Georgia join NATO.[103] General Baluyevsky said in 2012 that after President Putin had decided to wage the war against Georgia prior to the May 2008 inauguration of Dmitry Medvedev as president of Russia, a military action was planned and explicit orders were issued in advance before August 2008. According to Van Herpen, Russia aimed to stop Georgia’s accession to NATO and also to bring about a “regime change”.[83][104]

There is a direct cause-effect relationship for Russias invasion of Georgia and it seems that at the time France and Germany were aware of this, while Bush pushed for an escalation.

https://en.wikipedia.org/wiki/Russo-Georgian_War#Geopolitical_impact

The 2008 war was the first time since the fall of the Soviet Union that the Russian military had been used against an independent state, demonstrating Russia’s willingness to use military force to attain its political objectives.[287] Robert Kagan argued that “Historians will come to view Aug. 8, 2008, as a turning point” because it “marked the official return of history”.[288] The failure of the Western security organisations to react swiftly to Russia’s attempt to violently revise the borders of an OSCE country revealed its deficiencies. The division between Western European and Eastern European states also became apparent over the relationship with Russia. Ukraine and other ex-Soviet countries received a clear message from the Russian leadership that the possible accession to NATO would cause a foreign incursion and the break-up of the country. Effective takeover of Abkhazia was also one of Russia’s geopolitical goals.

The war also affected Georgia’s ongoing and future memberships in international organisations. On 12 August 2008 the country proclaimed that it would quit the Commonwealth of Independent States, which it held responsible for not avoiding the war. Its departure became effective in August 2009.[291] The war hindered Georgia’s prospects for joining NATO for the foreseeable future.[87][292] Medvedev stated in November 2011 that NATO would have accepted former Soviet republics if Russia had not attacked Georgia. “If you … had faltered back in 2008, the geopolitical situation would be different now,” Medvedev told the officers of a Vladikavkaz military base.

According to academic Martin Malek, western countries did not feel it was necessary to aggravate tensions with Russia over “tiny and insignificant” Georgia. He wrote in the Caucasian Review of International Affairs that Western policy makers did not want to alienate Russia because its support was necessary to solve “international problems”.[38] The May 2015 report by the Committee on Foreign Affairs of the European Parliament stated that “the reaction of the EU to Russia’s aggression towards, and violation of the territorial integrity of, Georgia in 2008 may have encouraged Russia to act in a similar way in Ukraine”.[294] The Russian invasion of Ukraine brought the memories of the Russo-Georgian War again into a broader geopolitical focus. In an opinion piece published in The New York Times on 6 March 2022, the incumbent Prime Minister of the United Kingdom Boris Johnson stated that Russia’s actions in Georgia in 2008 was one of the lessons of the past that the West has failed to learn

This isn’t just “Putin said”. There seems to be a quite clear understanding of that being the trigger point for Russia among foreign policy politicians and experts in Europe.