"You must bike on the road"

Here in France you cannot ride your bicycle on the sidewalks, I know that, but once in a while I do. Either when the roads really busy, or when there is no bicycle lane. And today as I was making my way home from my Butte-aux-Cailles tour I came to a red light. The intersection was empty... i'm on a bike, so I just went onto the sidewalk and crossed the street on my bike as a pedestrian.

So 2 seconds after I get across the street I hear "madamoiselle!". Huh? I think, me?? I look over and theres a cop on a motercycle pulling me over. Me... on a bike. Right! So he starts talking to me in french... and im like, "I dont seak french". Well unfortunately he knows english so he explains to me that...

1 - you can be fined for riding your bike on the sidewalk
2 - you can be fined for running a red light on a bike... which, he explains I did.
3 - my drivers licence can be taken away for running a red light on a bike.

Well! I was thinking, youve got to be kidding me!

Truthfully I knew that I wasnt supposed to ride on the sidewalk, but I pretended I didnt know. I also asked him some questions about riding your bicycle around France to make him feel like he had authority and that I was interested in him, respected his opinion and respected his countries rules. Finally after he explained things to me (I acted like, "wow, I never knew that, thank you so much for informing me", you could tell he liked that) he let me go, leaving me with " you must always ride on the road and obey all traffic signs".

"Always ride your bike on the road". That goes exactly against what I have heard all my childhood I thought as I continued on my way home.