I've been doing some reading surrounding the proposed Franco-British Union, and saw that British Prime Minister Anthony Eden rejected this idea. To quote Wikipedia, where I was doing the reading:
In September 1956, due to a common foe during the Suez Crisis, an Anglo-French Task Force was created. French Prime Minister Guy Mollet proposed a union between the United Kingdom and the French Union with Elizabeth II as head of state and a common citizenship. As an alternative, Mollet proposed that France join the Commonwealth. British Prime Minister Anthony Eden rejected both proposals and France went on to join the Treaty of Rome, which established the European Economic Community and strengthened the Franco-German cooperation.
Are there a particular reasons why Eden rejected these specific proposals?
There was significant entanglements related to the French that caused Eden to reject these proposals, most of them stemmed from sentiments from the time he was Foreign Secretary and considerations at the time also in play.
There was a few presumed and inevitable outcome that came with much closer social and political allegiances with the French. Most imperative and damning among them would be tying two very different types of colonial projects and the mannerisms in which they were treated together.
France unlike the British had separated itself much more heavily from the influence of the United States following the second world war with the express intention of maintaining it's colonial empire and autarky to the best extent possible. Conflicts like the 1st Indochina Conflict and the Algerian conflict were just ending and starting respectively by the time of the Suez Crisis in 1956 and neither bore well for the French. Long and diplomatically isolating conflicts were what brought Guy Mollet into attempting his shotgun marriage proposal to the British. Eden was quite aware of the risks of such engagements.
In addition to those more overt diplomatic contradictions between what the French sought and the British would benefit from on the matter. Eden also was of the opinion that France needed to cooperate further with Germany and the rest of Europe rather then retreat into the Entente rationale of the 1930's, Eden had taken a very strong stance on the European Defense Committee in favor of it. And was also a strong advocate to grant recognition to West Germany as a sovereign state. In this sense Eden held the traditional Churchillian cosmopolitan view of Europe. One that would be extremely integrated but without the presence of a British state.
At the time over 50% of British commerce was contained entirely in the Sterling Area whilst only a quarter was at the same time in Western Europe. It was considered more effective to keep Britain self contained with it's primary focus being on opportunities with the United States. At least in Eden's opinion.
There was a lot of other nuanced fields like the technicality of the French state being 100% integrated between the Metropolitan areas and colonial Empire that would've involved a colossal increase in social expenses for the British, and even more logistical problems like the remaining French obligations to states like Tunisia and Morocco that would have become joint British - French obligations.
I can't speak entirely to why Eden rejected French membership of the commonwealth. (Although it may have simply been the fact that France would have needed political capital to change itself to a Monarchy that Guy Mollet himself knew he couldn't bring to bear.) But the conditions and asterisks related to a full Franco - Anglo union would've been insurmountable due to their declining but still outstanding worldwide and political obligations.