Lost childhood media: "Mon ami, mon ami" song

 I have a song stuck in my head, and the only lyrics I can remember are "Mon ami" repeated over and over.

 

Mon ami, mon ami

Mon ami, mon ami

Mon ami, mon ami

Mon ami, mon a-mi 

The tune of this "mon ami" song can be heard here.

 

I am confident I've gotten the tune right, but less than 100% confident that the words I remember are "mon ami", or that "mon ami" are the only words. When I sing it to myself in my head it's in an anglo accent, which suggests, I first heard it before I started learning French in Grade 4.

 

Ring a bell for anyone?