Learn Polish: Lubię francuskie wino.

In Polish, adjectives describing nationality or origin are not capitalized. So while the country "France" is Francja (capitalized), the adjective "French" is francuskie (lowercase).

Lubię means "I like". Could I use podoba mi się in this sentence instead?

Not in this context. Lubić is used for things you enjoy consuming or experiencing, like food, drinks, or activities. You use podoba mi się when you find something visually appealing or attractive, like a beautiful car or a nice dress.

The verb lubić requires the accusative case. Why didn't the endings for francuskie wino change?

They actually did change, but the change is "invisible" here! Wino is a neuter noun. A handy rule in Polish is that for neuter nouns, the accusative case always looks exactly the same as the nominative (dictionary) form. The adjective francuskie follows the same rule.

I thought adjectives for nationality or origin usually go after the noun. Why is it francuskie wino instead of wino francuskie?

You are right that official or classifying categories usually put the adjective second, so wino francuskie is what you would see on a wine menu or in a shop. However, in casual everyday speech, Polish speakers often move the adjective to the front (francuskie wino) because it flows more naturally when just talking about personal tastes.