How did the Federalists and Republican view on foreign affairs differ?
I think that the Republicans viewed foreign affairs in a more isolationist manner than the Federalists. It is a challenge to assess what the Federalists would do in foreign affairs because at the time, there was little in way of Federalist leaders to fully articulate the point of view for the foreign affairs of the Federalists. Certainly, the Federalist intervention under Adams in foreign affairs in the X,Y,Z, affair and the passage of the Alien and Sedition Acts both caused public perception to side with the Republican point of view in foreign affairs. The Republicans, under Thomas Jefferson, were much more cautious in foreign affairs. They proceeded with negotiations with France via the Pinckney Treaty to acquire the Louisiana Purchase. Jefferson was very cautious and conservative in proceeding with this. The Republican point of view of embracing smaller and more localized governments would also lead towards an isolationist point of view in foreign affairs. Additionally, the Republican desire for neutrality in France and England Wars ravaging through Europe would also indicate how their point of view on foreign affairs is different than that of the Federalists.
After 200+ years from the Revolutionary War, many Americans today think our well known patriots and revolutionary leaders were all of the same ideals and concepts about forming a new country and government; but it wasn't really like that at all. We can point to many common themes we've been taught about religious freedom and not wanting to be taxed without a say in the matter, etc. The reality was, beyond wanting to be out from under the rule of the British Crown, the rest of everyone's wants/desires were VERY much open for debate; and debate they did for quite some time!
The Founding Father's first stab at writing a set of "rules" for our new country, The Articles of Confederation, actually had a broad spectrum of agreement amongst the new American citizens...no one liked them! The wording was so casual in most areas that it was difficult to accomplish even some of the more basic government functions.
All of these things led to a series of meetings we call the Constitutional Convention. There may have been a dozen or more centers of political thought when the discussions started; but it wasn't too long before two primary political groups began to emerge and set a course we largely still follow today. These two groups back then were known as the "Federalists" and the "Republicans." Generally speaking, these two groups align today with the Federalists similar to our Republican Party, and the Republicans are quite similar to the modern-day Democrats. Yes, it sounds like there's some name-swapping confusion going on with Republicans then and now being opposites. That's a whole different discussion for another day!
During the time of Presidents Washington, Adams, Jefferson and such, the two political groups had some very different ideas about running a government. Generally, Federalists were supporters of a strong presidency and a strong central government. The Republicans in those days wanted our central government to be given only certain, very specific areas of authority. The rest of the rules, expressly written, merely implied, or not yet considered, would all fall within the purview of each state deciding for themself what rules they wanted or didn't want.
Keeping the idea of a strong central government in mind, the Federalist's opinion on foreign affairs was the U.S. ought step-up on the world stage and be just as much of a big player as the other political powers in England, France, Spain, Germany, etc. The feeling was if we didn't put ourselves out there in terms of opening embassies, negotiating trade agreements, putting a strong navy on the high seas, staking claim to undiscovered lands, etc., we could just be swallowed up by one of the influential countries when they decided they wanted what we had.
Conversely from the Federalist's viewpoint, the Republicans felt we should be conservative on the world stage. We had a huge continent to explore with many natural resources waiting for us. The Republicans knew Europe was starting into the industrial revolution, but we didn't need all that. We had wonderful land for agriculture, etc. We should ignore the rest of the world's squabbles and problems; focusing on nation building for ourselves. In essence, we came to this continent to have our important freedoms; so that should be our focus.