The United States is one of the four major factions aligned with the Allies. When Paris falls, France becomes the United States. They will be given additional resources in which to rebuild their economy and five tier 5 cities in the north east corner of the map as well as a government centre. In addition, the United States will retain control of all the French colonies that have not been taken by the Axis. As the US you will also be given access to US units with different stats.
When Paris falls, the French player becomes the US. They can continue the fight immediately from the French colonies and cities that have not already been taken. In addition they are given a number of Tier 5 cities at the North-West of the map, representing America. There you can build up your income and industry in safety. The US is one of the most flexible countries to play and it is up to you where you want to fight. Build up a unit production center near one of your cities and take the fight to the Axis!