Do american and french school kids write on the same ruling all the years?
I might not be the best person to answer for American kids, as my "kids" are adults now.
In the early grades, the paper is turned landscape (sideways) and ruled with a rather wide rule, but I don't have the dimension. Also there is a dotted (or faint) centerline between baselines. It is the height used for body characters with no ascenders, c, e, m, etc. Ascenders and descenders are midway to the appropriate centerline or baseline, by eye, no line for guidance.
Later, they use paper in normal portrait orientation with only baselines ruled. Normally a wide rule is used in elementary grades. In high school and beyond, people would use a narrow or wide rule according to preference, where a narrow rule is about 0.25" or 6 mm. Various wider rules exist, 0.375", 8 mm, or 9 mm, based on brand and country of origin. One popular brand, Ampad, offers three rules, narrow, 1/4"; college 9/32"; and wide, 11/32" (6.3 mm, 7.1 mm, 8.7 mm).
This is basically my experience. I'm young, still in high school, so I probably have a fresh look on what the modern way is. I remember the really wide landscape paper. It was typically an ugly brown rough paper, like bad newspaper. The baselines were light red, the middle line was light blue, and there was lots of space everywhere. They were really wide. In the middle of elementary school years, we start to use wide ruled notebook paper. The lines were light blue, and there was a margin on the left hand of both sides as well as a margin at the top. The teacher made the rules on what you could do. The most strict would say no writing outside of the margins or on the last line of the piece of paper. I remember one teacher subtracted points if you went over the right side margin. But it's a hard to see margin, as you have to see it through the paper. But all in all, in America it's pretty loose. These days in high school, some teachers have rules but most things are just handed in on whatever loose leaf paper you have. College ruled is encouraged and sometimes required, but not always. You can use whatever note book you want and the biggest peeve of most teachers are the random scraps on the left side of a page when you rip it out of a notebook. Which is why perforated pages are now extremely common. Things get more strict when you have to type them (and much of the time, you HAVE to type it. No more hand written stuff!) There's many rules for that. As for handwritten stuff, most of the time you can often use any color pen or pencil you want "As long as [the teacher] can read it." I've written with crayon before. Many teachers correct with purple or green or whatever. Except for scantrons, those have to be #2 pencil! Though I hadn't seen a fountain pen in real life before I got one myself.
When I was young, many things had to be done in pen, a few things (math, mainly. Which still has to be done in pencil) could be done in pencil. These days more and more everything has to be done in pencil except formal essays, I hear, when dealing with elementary schoolers. My friend's sibling actually got points taken off for using pen! But that's in elementary school. As I said before, high school is really very loose. As long as it's legible, they don't care if it's cursive or print (though cursive is quickly becoming extinct).
In the end, the American schools I have been to may not have been strict enough, and that may explain a few things, but the French way described in this thread sounds awful.