Here are some ideas:
During the Chinese Civil War the Communists accept the defection of the 19th Route Army. With a much stronger base things snowball with the Communists, the left-wing of the KMT, and the left-leaning warlords forming an alliance against the right-wing of the KMT. THis results in a bloodier Chinese Civil War. The US throws their support behind the Rightists, although that support is limited due to the prevailing isolationism within US politics at the time. When Japan invades China they form an alliance with the Rightists (instead of IOTL where they formed an alliance with the marginalised leftists under Wang Jingway), and when Pearl Harbour happens the US drops their support for the rightists, but they have thoroughly burned their bridges with the Chinese government.
The FBU is formed after the German invasion of France. After the war ends, largely as IOTL, the Union persists and a Churchill/de Gaulle coalition is elected that is committed to preserving the position of Britain and France on the world stage, as well as maintaining their empires. Indian independence is shot down. Mass uprisings soon occur in India and Indochina, with the Chinese and Soviets pouring fuel on the fire, which results in a violent crackdown.
In the US Roosevelt is able to keep Henry Wallace on as VP in 1944, resulting in him coming to power in 1945. His attempts to cooperate with the Soviets, and his opposition to the violent crackdown by the colonial powers, which leads to him cutting off Marshal Aid, alienates the US from the European Empires, who rally around the FBU. Concerns over the rise of Communism result in him losing the 1952 Election to Harry Stassen, ending cooperation with the Soviet Union. Wallace's more cooperative stance with the Soviets also results in the US helping them to develop a nuclear deterrent, along with the Europeans.
In China, the leftist KMT turns on their Communist partners and violently purges them, although not before regaining Manchuria thanks to the then allied Soviets. This angers the Soviets who proceed to move troops into Xinjiang under the pretext of defending the Republic of East Turkestan, which is subsequently turned into a satellite, whilst arms and support are given to the Tibetans to "enact their right to national self-determination". In North Korea pro-Chinese forces are able to usurp control.
In Japan a four-way occupation is set up, with the Americans, Soviets, Chinese, and Franco-British all receiving occupation zones. As relations between the powers deteriorates, Japan ends up partitioned into four states: the pro-Soviet Peoples Republic of Japan in Hokkaido and Northern Honshu (with the Soviets giving them the Kuril Islands and Southern Sakhalin to bolster their nationalist legitimacy), the pro-Chinese Japanese Peoples Republic in Kyushu and the Ryukyu Islands, the pro-Franco-British Kingdom of Japan in Shikoku and Southern Honshu, and the pro-American Japanese Republic in Central Honshu.
In Germany the American occupation zone is merged with the OTL allied occupation zones in Austria, forming the South German Republic. The French annex the Saarland, and establish a Rheinland Protectorate. The FBU reorganise the OTL British occupation zone into the Kingdom of Greater Hanover. The Dutch are allowed to implement plan A of the
Bakker-Schut Plan. Berlin ends up divided three ways. The Soviet zone becomes the DDR as IOTL, and the Soviets also establish the Austrian Free State in their Austrian occupation zone.
In South Africa the National Party wins and begins implementing apartheid. Seeing the growing rift between the US and the European Powers, the Nationalist government breaks their ties to the FBU and forges a closer relationship with the US, which further strains said relations.
The Korean War breaks out when the pro-Chinese North Koreans invade the pro-American South Koreans. The Soviets condemn Chinese aggression, but stay out of it, whilst the Franco-British, too busy dealing with their anti-colonial uprisings, leave the Americans to fight their own battles.
In Greece the Communists and Monarchists fight to a stand-still, with the Americans agreeing to arbitrate peace talks. This results in Greece being divided between a pro-Soviet republic in the north, and a pro-FBU kingdom in the south, with the Soviets and FBU feeling that the Americans were unfairly biased towards the other side.
In Italy, because the right was divided between pro-FBU and pro-American factions the Communist led Popular Front were able to secure a plurality and form a government. This eventually leads to a short civil war, which ends with the country divided between a pro-American Sicilian Republic in the south, a pro-Soviet Workers Republic of Venice and Milan in the north-west, a pro-FBU revived Kingdom of Sardinia-Piedmont in the North East, and a revived Papal State serving as a neutral buffer between them.
Over the course of the Cold War the European Powers, led by the Franco-British Union desperately try to hold onto their colonies, becoming increasingly authoritarian in the process, China and the Soviets compete to become the leaders of the anti-Colonial movement, with the Chinese generally winning out and the Soviets more willing to work with the Americans. The Americans attempt to establish a Liberal Capitalist anti-colonial movement, but their attempts are undermined by their support of apartheid South Africa and legacy of supporting right-wing military juntas.