The title's pronunciation might sound like "Ne regret rien" to a non-French speaker, but it's actually "Non, je ne re-grette rien" where the first part "Non" (meaning "No") is very clearly pronounced.
Here's how the title breaks down:
* Non: Pronounced "Non"
* je: Pronounced "zhuh"
* ne: Pronounced "nuh"
* regrette: Pronounced "re-grette"
* rien: Pronounced "ree-en"
So, the full pronunciation is "Non, zhuh nuh re-grette ree-en".
The song's title is often shortened to "Ne regrette rien" in English, but it is a slightly inaccurate translation.