The notes should be "legato-tongued." This means the notes are connected smoothly, but there is still a faint definition at the start of each phrase.
When searching for "Poirot theme sheet music sax," you will find options for various skill levels and saxophone types. 1. Solo Alto Saxophone
Start the theme with a breathy subtone (low volume with lots of air) and build the volume as the melody climbs into the higher register. Digital vs. Physical Sheet Music