Which is correct--Louis' car or Louis's car?

They both are correct.

There are two accepted forms for possessive singular nouns that end with an s:

Add an apostrophe (') after the existing s at the end of the Word: Louis'

Add an apostrophe s ('s) after the existing s at the end of the Word: Louis's

Examples:

Louis' car is parked on Third Street.

Louis's car is parked on Third Street.