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The most important bit of background information here is that Britain spent that period dedicated to thwarting France (particularly its continental ambitions). This was the basic diplomatic split in western politics.
In the USA, the Democratic Party tended to be very suspicous of England (for various reasons, the most practical of which was the clash of its southern base with the anti-slavery movement in the UK), and more sympathetic towards France. The Federalists (and later the Whigs), had their base in the commercial cities of the NorthEast. These areas had very strong ties of trade, culture, and religon (and did I mention trade?) to England, and thus tended to be more sympathetic to England, and less so with France.
US foriegn policy tended to veer from one to the other, depending on which party was in power. For instance, the War of 1812 against Great Britain, and the very favorable Louisiana Purchase, both occurred during Democractic administrations.