My SO and I are currently staying in France under the country's visa long séjour, essentially a 1-year visitor visa. If we return to Europe after leaving when the visa expires we would naturally be covered by the Schengen visa for 90 days, which also begins the 180-day period. How do the rules for these two visas interact? For example, if we applied for another long séjour to begin at the end of our 90-day Schengen visa, does the Schengen period reset 90 days within the long séjour period? Will the French authorities frown on having visa types overlap like this? Our goal is to travel for around 2.5 years in Europe and then return home. We're American and can prove means and lodging for the entire period.
As far as the 90/180 day rule is concerned, days you spend in France under a valid French long-stay visa are treated like not-in-Schengen days. Everything else keeps running normally.
If you've been in France under the D visa for the last 180 days, you therefore have 0 days of your 90 day-allowance used.
we would naturally be covered by the Schengen visa for 90 days, which also begins the 180-day period.
There's no "the 180-day period". It's a rolling period -- or in other words, there's a 180-day period beginning every day and you need to keep to at most 90 days in each of those overlapping 180-day periods at once.
Will the French authorities frown on having visa types overlap like this?
As American citizens, it should not be possible for you to have a short Schengen visa; such a visa would not allow you do to anything more than you can already do without any visa. So there are no visa types to overlap.
Whether the French would be inclined to issue another long-stay visa if you've effectively been resident the whole time (no matter on which legal basis) is another matter. But you don't even say what the basis for such a renewed application would be, so it's impossible to predict how it would come out.