I assume you don't mean the attempts by the Romans, Byzantines under Justinian, Franks under Charlemagne, French under Napoleon, and Germans under the Third Reich. Rather, you're probably thinking of the modern European integration process.

Although the destruction wrought by the Second World War created an impetus to share resources in order to accelerate the reconstruction process as Europe was now faced with the threat of the Soviet Union, the roots of European Unity predate the cold war. Nationalistic fascism of wartime Europe had already spawned a reactionary opposition which favored the elimination of national borders in favor of a unified European federation. As this opposition emerged from exile and incarceration to find itself in charge of postwar reconstruction, the economic necessity of a coordinated European reconstruction process was easily integrated with the political desire for lasting European unity. Consequentially, European Integration was fueled not only by the search for prosperity, but also by an aversion to authoritarian oppression. The forces behind European integration, then, appear as a series of paradoxical juxtapositions: prewar ideas penned by antifascist idealists were adopted by postwar anticommunist pragmatists who resolved to compromise national sovereignty to maintain national relevance.

The seeds of European integration had already been sown by Europe’s antifascist intelligentsia immediately prior to the outbreak of the Second World War. As early as 1931 the French Foreign Minister Arstide Briand proposed a Pan-European federation, right as the German Nazi party was getting ready to win a plurality in the following year’s elections. In 1936 the socialist English writer Henry Noel Brailsford proposed a league which bore a strong resemblance to the structure eventually adopted by one of the predecessor institutions of the European Union, the European Coal and Steel community. After the rapid fall of France following the outbreak of the Second World War, Great Britain emerged as the primary pluralistic antifascist force in Europe, and consequentially the most fertile intellectual environment for ideas regarding a Pan-European federation to ferment. Proponents tended to emerge from the leftist camp, and included socialist London School of Economics professor Harold Laski, influential Fabian Society member and Oxford lecturer George Cole, as well as Times writer and former diplomat Edward Hallett Carr. These proposals did not go unnoticed by the opponents of fascism on the continent, and in 1941 an influential Europeanist manifesto was penned by Altiero Spinelli, an Italian communist organizer interned on the Island of Ventotene, with the collaboration of fellow exile Ernesto Rossi, a socio-liberal newspaper editor.

By August 1943, Spinelli and Rossi’s ideas had inspired the first European federalist organization: the Italian “Movimento Federalista Europeo,” (M.F.E.) which counted among its members many prominent activists of the “Partito d’Azione,” Italy’s largest group opposing the ruling Fascist party. Following the war, the presence of a Europeanist Party in every Western European country as early as 1946 attests to the desire to break with fascism’s ultra-nationalism, an understandable feeling since the consequences of nationalistic extremism were all too clear. Indeed, just like advocacy for Pan-Europeanism united both the communist Spinelli and the liberal Rossi, so did European integration find wide consensus among the two principal forces in postwar European politics: the progressive Socialists and Social Democrats as well as the conservative Christian Democrats.