May on Wednesday expelled 23 Russian diplomats, severed high-level contacts with Moscow and vowed both open and covert actions following the attack.
The diplomats must leave the country within a week.
Britain has linked the attack to Soviet-designed nerve agents known as Novichok, and accused Moscow of failing to explain how the poison came to be used on English soil. Before the exchange, he was serving 13 years in prison for leaking information to British intelligence. Russian Federation denied responsibility for the attack.
It also suggested on its Twitter feed that the United Kingdom could have the capacity to manufacture the nerve agent used in Salisbury.
She had given Russian Federation a deadline of last Tuesday evening to explain the use of the nerve agent. British ministers and royals also won't attend the World Cup soccer tournament this summer in Russia, May said.
Asked if she was confident Mr Macron was on side, a spokesman for the Prime Minister said: "He along with other European allies have been steadfast in their support".
U.S. Ambassador to the United Nations Nikki Haley continued her onslaught against the Russian Federation by condemning the European power for the poisoning of two people in a chemical attack carried out in the U.K.
The talks came after reports of a lukewarm response from the French government but Paris later issued a statement saying there was "no other plausible explanation" for the poisoning.
Paris's nuanced reaction has been in line with Macron's efforts since coming to office in May a year ago to build a new relationship with Russian President Vladimir Putin.
Britain, which has received statements of support from the United States, the European Union and North Atlantic Treaty Organisation, has said it will seek to coordinate an global response to the attack. In a rare joint statement, the leaders of Britain, France, Germany and the USA on Thursday condemned the attack on Skripal and his daughter Yulia as an "assault on United Kingdom sovereignty".
"It is predictable that Russian Federation will expel 23 British diplomats if they have 23 diplomats in Moscow".
Britain claims the father-daughter pair was exposed to a nerve agent and Russian Federation is responsible for the act, which Moscow denies.
The attack on him was likened in Britain to the killing of ex-KGB agent Alexander Litvinenko, a critic of Putin, who died in London in 2006 after drinking green tea laced with radioactive polonium 210.