The Franco-German rivalry is centuries old and dates back to wars over Alsace-Lorraine and the Franco-Prussian war set the stage for the two World Wars essentially. Why then did DeGaulle and Adenauer get along so well in postwar Europe? Was it because of communism?
It was partially because of communism, yes, but also because of De Gaulle and Adenauer specifically.
I am rarely a friend of great man history, but in this case, you have two thick-sculled authoritative (and, some would argue, authoritarian) leaders on your hands that have a certain interest to work together.
Now, the personal friendship between De Gaulle and Adenauer was legendary and I am willing to believe that these two actually really liked one another, but as the politicians that they were, they were in it for their respective country.
So what did each country have to gain? What was France's perspective? What did the West Germans think?
#France
So, me being a francophile German guy, let's talk about the French first. Whereas West Germany was a state recovering from total annihilation during wartime, France tried to hold on as a world power in a modernized global society that had moved past the European colonial empires of old. France was engaged in a costly War in Indochina between 1946 and 1954, and suffered a most painful defeat at the hands of Ho Chi Minh's insurgents.
But more decisive than the conflict in Indochina was the Suez Crisis of 1956. You see, the French had formed a new "Fourth Republic" after World War II to make a clean cut after the Vichy Regime hijacked the legacy of the Third Republic after the French armistice with the Germans in 1940.
The Fourth Republic needed results, and Egypt's aspirations to nationalize the Suez Canal proved to be the opportunity for France to prove to the world and, perhaps more importantly, to itself that the French were still among the top powers in the world. The public had not taken the humiliation in Indochina well, so Egypt seemed like easy pickings to regain political momentum for the Fourth Republic. The Guy Mollet administration forged a secret agreement with the United Kingdom and with Israel, and in late October of 1956, the three countries in a swift operation occupied the Suez Canal.
But the success was short-lived: Although most nations at the time approved of the three nations' dealings under the condition that the Suez Canal would remain under international oversight, two critical players did not. These two critical players taking Egypt's side in the matter were the United States and the Soviet Union. Both of them were keenly aware of the importance that the Middle East would have for the upcoming decades, and both sides much preferred a Suez Canal under Egyptian control with Egypt firmly aligned with their respective camp than having an unpredictable (and, from the Soviet perspective, likely unfavorable) international committee overseeing things. Taking a stand against Nasser would have also meant taking a stand against all Arabs in the region, and neither Eisenhower nor Khrushchev were looking ahead to that at all.
And thus, the United States demanded that its three allies stand down. The UK complied almost immediately, with the Anthony Eden administration already having faced considerable discontent at home regarding the sudden and unprovoked military action against Egypt.
Israel also complied, retreating from the area. France, now standing alone, was forced out as a result - the international coalition had been lost. Where Israel and especially the United Kingdom were taught the lesson of always complying with their nations' respective relationship with the United States and always cooperating with them, France sought distance, feeling stabbed in the back by its own military allies.
The result of the humiliation at Suez was the collapse of the Fourth Republic - as Charles De Gaulle was called back from retirement to lead the nation, he demanded constitutional changes to various offices that would effectively create the Fifth Republic when the 28 Oct 1946 constitution was thrown out and replaced by the one of 4 Oct 1958.
France in general and Charles De Gaulle in particular had aspirations to become the leading power in the new European system - a leading France assisted by a strong West Germany, surrounded by a handful of smaller states around them.
#West Germany
The West Germans meanwhile were still trying to regain their footing. Konrad Adenauer had been elected the country's first chancellor in 1949 and would hold that post until 1963. The economic miracle ("Wirtschaftswunder") of the 1950s saw a rapid rise in employment and an economic expansion that was unheard of elsewhere - for example in East Germany.
Adenauer followed the policy of Westbindung, western alignment. The christian conservative Adenauer had presented this model against the neutrality concept that was popular with the social democrats - as a neutral and disarmed Federal Republic would have had chances to perhaps reunify with the also disarmed and neutral Democratic Republic in eastern Germany rather quickly.
Adenauer torpedoed this (already quite unrealistic) hope with his electoral victory and immediately set to get a few things done:
Economic Recovery
Diplomatic Reconciliation with the UK, the USA and France
Path to NATO membership and the formation of a standing army for West Germany.
And, as it happens, in all these things, the most useful asset to Germany would be a strong friendship with France. It would take until the collapse of the Fourth Republic and the French turn away from the UK and the USA for the true "Deutsch-Französische Freundschaft" (quote by Charles De Gaulle holding a German-language speech to the West German audience) to become reality, but Adenauer already sought the support of Paris for a continental union for coal and steel trade. The European Coal and Steel Community, abbreviated ECSC, was formed between West Germany, France, Italy and the BeNeLux states in 1952 and made history as the first treaty with a supranational governing body - a central commission that could make binding decisions for all member states.
Of course, this ECSC would be replaced by the European Economic Community EEC in 1957 and would from that form eventually merge into its 1992 and current iteration, the European Union.
So that's the basic overview.
France wanted a secure European market and influence zone out of the reach of both UK and USA.
France needed diplomatic successes after the debacles in Indochina and the Suez.
France, anticipating the threat of decolonization of its remaining colonies, was interested in forming a safety net to make up for economic losses as soon as possible.
France wanted access to West Germany's well-affordable coal thorugh a free market.
West Germany wanted to align with the democratic west.
West Germany wanted the right to rebuild its army.
West Germany needed economic recovery.
West Germany, in order to beat East Germany and to force East Germany to eventually be absorbed into West Germany, needed to be completely and utterly dominant over East Germany in all aspects, especially economics.
West Germany needed access to a free market zone with affordable French steel.