Moscow denies responsibility for the attack on ex-spy Sergei Skripal and his daughter Yulia.
It was the same evidence that failed to persuade Labour leader Jeremy Corbyn to pin the blame on the Kremlin.
May has until now encountered significant resistance from Europe. But in traditional European Union style, they agreed to the latest text after extracting concessions on other issues - in this case, wording critical of Turkey's actions in the Eastern Mediterranean and the Aegean, the site of tensions over drilling for gas.
But divisions remain over how far to go, with Austria already ruling out expelling diplomats, and Tusk, a former Polish prime minister, said it was not clear how many states would join the expulsions. It noted with obvious concern that "despite worldwide sanctions on Russia for its annexation of Crimea and perceived role in a pro-Russian uprising in Ukraine, trade between Germany and Russia grew dramatically in 2017", citing the particular importance of "increased demand for Russian natural gas and crude oil" and Germany's backing for the Nord Stream II pipeline "that would double gas supplies from Russia to Germany..." German chancellor Angela Merkel has shown her support for the French president's decision.
Donald Tusk, President of the European Council, said the expulsion of Russian officials from member states "is not the end of our actions".
The issue of relations with Russian Federation divides European Union nations sharply, and there is pressure from some to lift economic sanctions against Moscow, so Britain has not pressed for additional steps of that kind.
The 28-nation European Union has recalled its ambassador from Moscow for consultations, and several countries, including Lithuania, Latvia and the Czech Republic, say they are considering expulsions.
Mr Macron, who was initially criticised for a lukewarm response to the attack on 4 March, said: "We consider that this is an attack on European sovereignty".
Merkel declared that sanctions "are necessary", but did not specify what they would be. Britain says the expelled Russians, who left London earlier this week, were undeclared intelligence agents.
Danish Prime Minister Lars Lokke Rasmussen said his government heard the "strong signal" from the bloc's leaders. France, Germany Poland, the Netherlands, Estonia, Latvia, Bulgaria, the Czech Republic and Denmark were also believed to be preparing a similar move.
A court on Thursday approved a request for worldwide chemical weapons experts to take a sample of their blood to check the UK's view that they were poisoned with the novichok nerve agent.
She reported positive identification of the world's leading experts military lab at Porton Down chemical agents used as part of a group, nerve agents are a novice.
He said the Kremlin specifically regrets the "recall [of the envoy] for consultations". The tests were conducted by British military chemical weapons scientists.
Irish foreign minister Simon Coveney later revealed his country would carry out a "security assessment" on all Russian diplomats as part of the consideration of "additional measures".