During the early stages of world war II, Adolf Hitler, Germany's leader and its Führer, planned and successfully executed the invasion of France which, in the wake of its crucial defeat in 1940's "Battle of France", fell into the clutches of the Nazis in a matter of weeks. In the aftermath, France was not only coerced to formally surrender, but to sign the France-German Armistice of June 22, 1940 as well.
This victory, for the jubilant Third Reich, was a striking triumph on account of its significance and outcome: first, they vanquished one of Germany's main, neighbouring enemies that was among the first to declare war on the Nazis following the latter's invasion of Poland in late 1939.
Second, France's defeat and eventual surrender were, of course, a major blow that shattered the Frenchmen's pride. Yet just as degrading was the Armistice they were compelled to sign, which in reality, was closer to an annexation treaty; basically, it divided France into two zones: a German occupied military zone in the North and west, while the remainder, roughly two fifths of the country, was left to the French in full sovereignty. Or at least, nominally so.
Last but not least, and by the establishment of the occupation zone, Hitler was granted what he was longing for: a firm foothold the Nazis could exploit as their base to sweep Western Europe as a whole. A region which they already began to subdue at that point.
In short, the Battle of France was a "hitting several birds with one stone" kind of victories for the Germans. However, on the other side of the equation, the lost battle brought France on its knees, rendering it under the mercy of the merciless Führer. And despite the subsequent attempts of the French resistance, their country would remain occupied for the longer part of the WWII.
On the other Bank of the English Channel, the English officials were disgruntled, if not appalled, by the German encroach upon the French territories and sovereignty. Not at least for the humiliation they sustained when the Nazis forced the British troops off the content. But furthermore, they feared the serious repercussions of the occupied zone which, due to its closeness, became an ideal starting point of the German attacks on the British isles, and hence, a perpetual threat to Britain's safety,
By 1944, for this and other reasons that goes beyond the scoop of this article, the prevalent atmosphere in the region, as in the whole world, was one of tension, and an other brutal, decisive battle was in the wind again: liberating France, foiling Hitler's plans and put a stop to his overgrown power and ambitions in conquering Europe were the aim for England and its allies. Though on the Germans' end, it was to tighten their grip on Western Europe and go on with conquering the remainder of the content with little to no resistance.
On June 6, 1944, roughly a few days before the fourth anniversary of the "Battle of France", Britain, alongside the United States and Canada mainly, launched the " Operation Overlord", a codename for what would be commonly known as "The Invasion of Normandy" or simply the "D-day". With the objective of liberating the German-held coast of northern France, this allied onslaught consisted in landing over a 156 000 troops on the coast of Normandy in the early hours of morning, and was associated with airborne operations to ensure the mission's success.
I deem it noteworthy to showcase the fact that the amphibious invasion was, and still is, the largest of its kind in history, and is a testament to how crucial this operation was in changing the course of WWII.
After nearly 3 months of ferocious battles, bloodshed and a death toll in the aftermath that, depending on the source, fluctuates between 25000 and 39000 belligerent and civilian, the Invasion of Normandy resulted in the Allie's victory and a full retreat of the Germans out of France, leaving behind dozens of thousands of captured soldiers in the hands of fate.
Essentially, this battle was fundamental as it paved the way to liberate all Western Europe afterwards. But also on account of its repercussions on the Third Reich which was never resilient enough to endure the costly loss of territories and therefore the natural resources, especially with several taxing battles ongoing on other fronts.
In hindsight, this defeat was the beginning of the end of Nazi Germany, for it was one of many defeats to come that, hand in hand with the wrong choices he made, inexorably led to Hitler's downfall less than a year later.
In 1949, four years after the WWII came officially to an end, Germany was on the brisk facing the ill fated consequences of losing the war. As fate would have it, and for occupation purposes, the country was decided into four zones by the four main Allies: Britain in the northwest, France in the southeast, the United States in the South and the Soviet Union occupied the East zone. The British, American, French zones combined made up Western Germany, while Eastern Germany comprised the Soviet zone.
This partition, as such, was much more than a "fitting" settlement of a dispute, or a mere "punishment" to the Germans for their "deeds"; it basically mirrored the unspoken feud between the communist East and capitalist West. Consequently, the partition was a sufficient condition for the emergence of the cold war, the center of which was an already torn to shreds Germany where all had to be rebuild anew. Needless to say, as the primary scene of the weaponless clash between the West and East, when the divisions between the two became more pronounced, so did Germany's division, rendering its two parts almost two entirely different countries. This would remain the case until the collapse of the Soviet Union forty years later.
In the meanwhile, and due to England's essential role in liberating France, the diplomatic relations between the two flourished as both countries became close allies and on very good terms, which in 1994, culminated in the construction of the "Channel Tunnel"; a partially submerged tunnel across the English Channel that links England, throughout France, to the European continent. The tunnel is claimed as one of the modern world wonders.
Keep in mind though, the idea of linking both countries is nothing new and dates back to the days of Napoleon. Back then, the English flatly refused the project lest, and perhaps rightly so, the French emperor would use it to invade England.