By all appearances the Battle of Bouvines should be a defining moment of the middle ages, yet I never hear it referenced. It sounds like something from a fantasy novel: the English Angevins, the HRE Emperor Otto IV, the lowlands including Flanders, Brabant, Holland and Lorraine ally to neuter the French King Phillip Augustus. Phillip carries the Oriflamme battle standard, said to come from Charlemagne himself, to the field of battle, outnumbered and opposed by Otto IV clad in golden imperial armor.
The battle opened and was decided by a charge and melee of mounted knights, where Philip himself charged with his reserves, was unhorsed and after a long fight drove back the Flemings, took the center and captured Otto's imperial eagle standard.
Politically, Otto lost the emperorship to a Hohenstaufen, the Angevins lost most of their continental empire and were forced to sign the Magna Carta. We can imagine a very different course of history had the French knights lost that day.
Where does this event stand today in the history of Western Europe? If I hadn't stumbled across it in Wikipedia, I may never have learned of it at all.
Well, the short answer is that it is and incredibly important event, just one perhaps not often recognized in popular english-speaking media. I can easily reel off several films based on the contention surrounded the Magna Carta, but it is significantly harder to do so about the Battle of Bouvines.
At the same time however, I would say that academics are quite aware of the massive importance of Bouvines. It had all the consequences you mention, and was a major turning point in the career of Phillippe Augustus. One should mention that Phillippe is partly called "the Great" because of massive success at Bouvines and afterwards. And like you mentioned, it was part of a slew of events that eventually led to the signing of the Magna Carta, an important step to the development of the English parliamentary system.
I think the one of the greatest lessons one can learn from Bouvines is that the English strategy of shirking their responsibilities militarily on the continent by relying on allies in the low countries and Germany was not a workable one. It took large physical commitment of English troops under english commanders to gain any serious victory on the continent, for instance with Edward III in France during the Hundred Years War.
Sources:
The government of Philip Augustus: foundations of French Royal power in the Middle Ages. University of California Press. 1986
Halfond, Gregory I (2015). The Medieval Way of War: Studies in Medieval Military History in Honor of Bernard S. Bachrach
Frank Barlow The Feudal Kingdom of England 1024-1216