Moore says that the British and French intelligence services are collaborating to "assess the risks" of Russian President Vladimir Putin's blend of "fury and aggression".
In a speech in Paris to diplomats and intelligence agents, Moore warns of the fear that Russian sabotage can instill in vulnerable countries and their support for Ukraine.
Putin will not stop if he is allowed to succeed in making Ukraine a vassal state, says Moore, and warns that countries like China, Iran, and North Korea will form closer ties with Moscow in the event of a Russian military victory.
France's intelligence chief for DGSE, Nicolas Lerner, warns at the same gathering that "Europe's collective security is at stake" in Ukraine.
The speeches on Friday were held in connection with the two countries celebrating 120 years of intelligence cooperation in the Entente cordiale pact.