I believe they use the word “la toile” (the canvas?) for the internet. I’ve heard it on the news and on the radio in France. That being said, your colleague probably didn’t have any problem understanding your sentence, which is completely correct too. Everybody there understands “internet” and “web”.

Among my colleagues, “surfer le web” is completely legit too – no qualms about taking English verbs and making them into French verbs. “Surfer l’internet” also works.

I also just found this.

"En me baladant sur Internet / sur le web" is perfect, and probably what I’d personally use. Here’s a few more :

J’étais sur Internet, et je suis tombé sur…

En navigant sur Internet, je suis tombé sur…

En surfant sur Internet, je suis tombé sur…

"Le web" can be used instead of Internet.

Something I use a lot is:

Traîner sur internet

It means “to hang out”, with no particular goal, just to be there. It’s a great word if you want to get the idea of “killing time”.

“Naviguer” and “surfer” sound a little too “academical” to me. If you don’t want any negative (time-killing) vibe, “se balader” is fine, or just “j’étais sur internet“.