How did american debates about foreign policy in the 1790s reflect the beliefs of the political parties?

The two prominent parties of that period were the Federalist Party and the Democratic-Republican Party.

The debates at that period were held about the French Revolution, France and Britain. The Democratic-Republican Party's goals were a weaker central government and the emphasis on republicanism so they preferred the revolutionary France over relationships with the monarchy of Britain.

The Federalists were the opposite spectrum. They supported a strong central government, thus they supported federalism which put more emphasis on the central government more than the individual states. Thus they saw the French revolutionaries as anarchist and the threat to social order and religion. So they were more up for the relationship with Great Britain.