plates

Mes plus plates excuses.

My sincerest apologies.

— Le Patient anglais (1996)

Il allait marcher sur nos plates bandes.

He was going to step on our toes.

— Drive (2011)

Je te dois de plates excuses.

I owe you a profuse apology.

Je te présente de plates excuses.

I sincerely apologize to you.

Je vous dois de plates excuses.

I owe you a sincere apology.