The problem is that France did not award the Légion d'Honneur to the City of London, but to "London".
“Through the example of the Royal Family and the British Government, through the kindness of Londoners and the welcome they always bestowed on the French, through the solidarity and moral strength demonstrated by its inhabitants, London enabled Free France to be established. London, capital of the United Kingdom, which had become a symbol of the defence of freedom, a city whose very name restored hope to the French people under the yoke of the Occupation and which they forever associated with Radio London, deserved the gratitude of the French Republic. The French people know what they owe the British people, and will never forget it.”
This raises all sorts of issues. The City of London is not London. It is a small enclave in an area known as "London", but consisting of many local authorities. The area now controlled by the Greater London Authority is not the "London" that was controlled by London County Council during World War 2. Nor is/was London "capital of the United Kingdom". If anywhere could claim that title it would I suppose be the City of Westminster.
The arms of London County Council during the Second World War were these: