Why didn't France adopt the longbow like England did?

That's a bit of an oversimplification. China was much closer to the Mongols' logistical base. By the 1240s, as the Horde pushed into Central Europe, they were experiencing rebellions in Asia that threatened their supply lines. So extended sieges were not feasible.

It's telling that the limit of their incursions pretty closely adheres to the boundary of stone fortification diffusion in Central Europe at that time. Polish and Russian nobles still favored wood fortifications, though Western Europeans had brought back defensive masonry techniques from the Crusades and rapidly developed stone castle infrastructure in their home regions. Stone fortifications increased the time required for a siege and increased the cost in men and material, even with the Mongols' relatively effective siege tactics. The Mongols could not afford to conduct such sieges so far from their logistical base on the steppes, especially not while maintaining control of their often fractious conquests in Central Asia and Russia.

So it's a confluence of factors that limited the Mongol advance, including the relatively challenging terrain of Central European mountains and forests and the increasing frequency of heavily fortified stone-walled fortifications as they pushed farther west.

That said, outside the particular example of the 13th century Mongols, the effectiveness of steppe light cavalry against fortified European cities is at best questionable. The Avars and Hungarians were defeated by western nations once they attempted to push into fortified territory, despite the lack of stone fortifications in 9th and 10th century Europe. And, as you say, it was the incorporation of Chinese siege tactics that permitted the Mongols to succeed against fortified cities, not their prowess as light cavalry archers.

Later, by the end of the 15-th century, most of them were reunited under the rule of either the Grand Duchy of Lithuania or the Grand Duchy of Vladimir and Moscow (which would, two centuries later, become what we know today as Russian Empire, or Russia).

Anyway, Mongols had no problems crashing both quite a few times between 13-16 centuries. :-) Every state there was in the region back then had to paid the Horde.

This has happened quite a bit throughout history, actually. Complete social collapse, as has happened many times throughout history, can have a really bad effect on technological innovation. Focusing specifically on the Roman empire (because that's what I'm more familiar with), here are three off the top of my head:

* The various methods to making various different kinds of concrete have been lost and rediscovered several times [0]. Early concrete-like materials were used as far back as 6500BC by the Nabataeans. In both Roman and Egyptian times it was re-discovered that adding volcanic ash to the mix allowed it to set underwater. The Roman methods for making concrete were lost again following the collapse of the Western empire and were not rediscovered in Europe until the 1400s.

* Roman roads were extremely well engineered [1], to the point that some are still around today. While this wasn't "lost" per se (we could always go dig up a Roman road and see how it was made), the Roman road system in Europe deteriorated because of lack of resources and skills to maintain them. [2]

* The Romans made extensive use of plumbing [3], but much of that was again lost in Europe after the fall of the Western empire. The Roman Empire had indoor plumbing, meaning a system of aqueducts and pipes that terminated in homes (at least of wealthy people) and at public wells and fountains for people to use. [4] Lead pipe was used (okay, so maybe that part wasn't so great), and there were sewer systems [5]. Even the word "plumbing" derives from the Latin word plumbum for lead. Following the fall of the Roman Empire, plumbing development virtually ceased for centuries except for isolated cases of plumbing installed in palaces and castles.

These three things are so integral to the modern world we probably don't even think about them much, just assume they were always there. But not too long ago (at least on the scale of human civilization), they weren't.

TL;DR the Romans were awesome engineers.

[0] https://en.wikipedia.org/wiki/Concrete#History

[1] https://en.wikipedia.org/wiki/Roman_roads#Construction_and_e...

[2] https://en.wikipedia.org/wiki/History_of_road_transport

[3] https://en.wikipedia.org/wiki/Sanitation_in_ancient_Rome

[4] https://en.wikipedia.org/wiki/History_of_water_supply_and_sa...

[5] https://en.wikipedia.org/wiki/Tap_water#Pipe_materials

"Figure 1 illustrates a yew trunk cross section and how a longbow stave was carved out of the tree to incorporate both its sapwood and heartwood components. The former was used on the bow’s back, which faced away from the archer, taking advantage of the fact that flexible sapwood performs well under tension. The latter was used on the bow’s belly, which faced the archer, taking advantage of the fact that hard heartwood performs well under compression. Together the two types of wood created a natural composite bow that, when made from a long and thick stave, was remarkably powerful."

So, nature glued the parts together.