Learn French: « C'est ma meilleure réplique », murmure le protagoniste. - "This is my best line," whispers the protagonist.

This is a reporting clause, also called an incise. In written French, when a clause like "he said" or "whispers the protagonist" follows or interrupts a quote, the subject and verb are almost always inverted. Notice that unlike some question inversions, this inversion happens directly with the noun subject (le protagoniste) rather than adding a pronoun.

Does réplique always mean a line in a movie or play?

Not always! In everyday conversation, une réplique usually means a reply, a retort, or a comeback. However, in the context of theater, literature, and cinema—as hinted at by the word protagoniste—it specifically translates to an actor's "line" or "cue".

Just to refresh my memory, why is meilleure placed before the noun réplique?

Meilleure is the feminine form of meilleur (better/best), which acts as the comparative form of bon (good). Adjectives that describe goodness or badness belong to the small group of common, short adjectives that systematically precede the noun in French.

Notice the comma after the closing quotation mark. Is this standard in French?

Yes. Unlike American English, which often puts commas inside quotation marks, French punctuation places the comma outside the closing guillemets (« ») when connecting a quote to a reporting clause like murmure le protagoniste.