There have been periods of human history within some groups that did have no needs scarcity. Shelter, food, water, all there. Replenishing faster than they could consume it.

Which periods are these?

I'd say right now we have the necessary resources to provide for everyone's needs in the world. Providing for basic needs isn't a scarcity issue, it's a resource allocation issue. We aren't prioritizing providing for everyone's needs before providing for people's wants.

I'm lucky enough to live in a developed country, I have shelter, a fridge full of food, I turn a tap and I have potable water. It's all there for me. My needs are taken care of. I still think would be awesome if I owned a private island in a nice climate, with a big house on it and a pier with my own yacht I could sail around when I feel like it. But there's the problem, how do we determine who gets what they want? If I got the private island, yacht, etc. while you only had your basic needs met, would you consider that to be an equitable society?

Why does Picard get a vineyard in France while someone else has to be satisfied by whatever the replicator provides them?

TNG makes it clear that Picard values original artifacts. There's a scene where he assumes an artifact someone is giving him is replicated but then is told it's the original. He basically pisses his pants over it being a much too valuable of a gift. So no, in Star Trek people do place greater value on non-fungible items. You don't even think of this scene as unusual because of course people think that way.

Starfleet needed more starships to defend themselves from the Dominion. Do you consider that a need or a want? They don't have an infinite number of starships. Apparently building starships involved some kind of scarce resources.

Because they didn't have enough starships, a lot of people died. If we consider not being vaporized by a phaser to be a need, the Federation was not able to provide everyone's needs because of a scarcity of resources limited the number of starships they could produce.

Like I say, Star Trek is incredibly inconsistent about this. If an episode requires scarcity of resources so Nog can trade different things to different people in a fun episode, then those resources are scarce. If they need to use gold pressed latinum, they use currency. If someone asks "how does your economy work?" then suddenly "they don't use money, they don't need it because they have everything they want." And this is fine, if someone 300 years ago were to write some fiction about our time, it would probably be about people more Scrooge McDuck (who had a giant vault of shiny coins) rather than Elon Musk (who has no need for that because that's not how the economy works). Star Trek can't have a realistic economy, and it doesn't need it. We're just meant to assume it's broadly equitable, everything is fuzzy beyond that.

This is the case where if I were to replicate it, what would be the difference?

You can't replicate an infinite amount of land in France. You can't replicate an infinite number of private islands. People will value these things and they will be scarce. Why would Picard live on a vineyard in France instead of in a holodeck version of a vineyard if there was no value to the real thing?