This message is a conspiracy consistent with recurring pro-Kremlin narratives about the West's anti-Russian activities and attempts to disrupt Russia's relations with allies.
The founding treaty of the Eurasian Economic Union (EAEU) was signed by Belarus, Kazakhstan and Russia on 29 May 2014, followed later by Kyrgyzstan and Armenia. The EAEU came into existence on 1 January 2015. Its establishment, however, has nothing to do with the reasons for the EU"s sanctions against Russia. The first round of EU sanctions against Russia was introduced on 17 March 2014. The first bans and freezes assets were imposed on individuals involved in actions against Ukraine's territorial integrity following Russia's illegal annexation of Crimea. Later, in July 2014, in view of Russia's actions destabilising the situation in eastern Ukraine, the EU imposed economic sanctions and reinforced them in September 2014. In March 2015, the European Council linked the duration of those economic restrictions to the complete implementation of the Minsk agreements.
The Council of the EU is clear in this respect: "Since March 2014, the EU has progressively imposed restrictive measures against Russia. The measures were adopted in response to the illegal annexation of Crimea and the deliberate destabilisation of Ukraine." Read more about the EU's sanctions against Russia over the Ukraine crisis.
You can read earlier disinformation cases alleging that 'old' EU member states introduced sanctions on Russia after the provocation of the downing of MH17 by Ukraine here.