Nope. Entente Cordiale had been signed in 1904 and Franco-Russian alliance was strictly about the help against Germany and AH.Russia and France have common concerns against Britain?
Britain was openly and rather actively anti-Russian (helped to build Japanese navy and actively supplied it during the RJW ) while formally being neutral but Russia was not anti-British: even allowed the British observers to be present in the Russian army during the war.
If anything, the British entry into the RJW may force the Russian government to review the French alliance and to get close to Germany: Treaty of Bjorko proposed by WII stipulated mutual help in Europe against any European power which was better for Russia than a more narrow agreement with France.
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