There were both practical and ideological reasons why American leaders viewed "a well regulated militia" favorably in the 1780s/90s. I'll try to quickly sketch out both here.

First, the practical. The young United States was in an extremely tenuous military position in the late 18th century. The government effectively had no standing army, yet faced persistent conflict with Native Americans all throughout its massive western backcountry. These Indians were experienced fighters, as many had fought against the American colonists during the French and Indian wars and against the American rebels in the most recent conflict. Native American alliances were able to heavily defeat several American forces in the Ohio territory during this period. Indian resistance was aided and abetted by the hostile British, who held not only Canada but forts at Niagara and Detroit which they were supposed to have evacuated at the end of the war. Tensions on the New York-Canadian border were particularly high, as many displaced loyalists and Iroquois had settled in the region. An established militia system was the only politically and economically feasible way to fend off Indian "aggression" (really, resistance) and dissuade any invasion into American territory.

More philosophically, many political thinkers of the period thought that militia service was a moral virtue. These thinkers idolized (and idealized) the militaries if the Ancient Greek city-states and the early Roman Republic. In these societies, the duty of defending the polis from aggression (theoretically) was shared by all able-bodied citizens as an act of civic responsibility. The best citizens, said the likes of Jefferson, were those that could rely on themselves for economic subsistence and defense. This independence would allow people to focus on what was best for society, rather than what was politically expedient to gain power within the state. This was much preferred to a standing army controlled by a central government, whose soldiers, largely composed of the most poor and dependent members of society, would enforce any government act, no matter how unjust, without question. Thinkers did not have to look to antiquity for an example of this, as precisely this had occurred in England under Cromwell. An active militia both eliminated the need for a standing army and provided citizens a mechanism to resist one should the government ever create one.

Sources: Bernard Bailyn, The Ideological Origins of the American Revolution

Jack P. Greene, The Constitutional Origins of the American Revolution

Jack Kirby Martin and James Lender, A Respectable Army

Alan Taylor, The Civil War of 1812

Not necessarily. It was mostly in response to British violation of what the colonists viewed as rights.

In mid-1700s, prior to the Revolution, national defense in the colonies was mostly done by militias, both local and colonial. When anti-British sentiments arose, the British government embargoed arms shipments and sought to prevent the formation of "patriot" militias (as opposed to the "loyalist" ones that were more pro British). This increased ant-British feelings of most colonists, who objected base on two main reasons. The first was common law self-defense. You have the right to defend yourself and the right to own the tools to do it. The second was the general idea the The People have the right to collectively defend themselves. Sort of a "home rule" sentiment as opposed to Great Britain deciding whats best for the colonies.

Fast forward a decade. The war is over and the US is united under the very weak Articles of Confederation. The federal government had almost zero power in legislative ability. But also in military ability. At the time, the US standing army was around 100 guys and the Navy completely disbanded. This was one of the problems the new Constitution was supposed to address. The causes of the revolution left a sour taste for the idea of a more powerful government with a standing army to enforce things. But likewise, most easily foresaw that in any necessity to prevent European encroachment in the Americas, the state militias and guards would never be able to work together effectively. The right to keep and bear arms was again, put in there to solidify personal self-defense. But also as a method of allowing the states or the people to have a check against federal over-reach.

While Britain was the prime motivation for a stronger self-defense force, France also still controlled half the North American continent and Spain controlled lots of the Caribbean. In either case, most sources point to the 2nd amendment being much more entangled with internal politics of States & The People vs Federal Government than focused on another country intruding in US interests.