France has had some true high points in its history, chief of which was its ongoing feud with England, for control of Europe, and any new territories found by either one of them. This continual spat of neighboring countries, occasionally cooled off long enough for royalty from one, to marry royalty from the other, and then war would break out again.
But the highest point in the country is Mont Blanc, located in the Alps on the France-Italy border. In fact, its very location is a source of dispute, only this time with Italy. La Dame Blanche, or The White Lady as she is also known, is 15,780 feet high, give or take a couple of yards, depending on that year's snowfall. And both sides want that snow for themselves. France and Italy each claim ownership of the mountain's peak, even though there is a historical record that says it is divided between the two, exactly at the top.
An 1861 treaty between France and Sardinia in Turin, set the border down as being on the highest peak of Mont Blanc. Which means they share it equally, even though French maps often show the mountain to be almost entirely inside France.
The one thing the two countries did agree on, was the building of a tunnel under the mountain, which was completed in 1965. It connects the cities of Chamin, Haute-Savoir in France, and Courmayer, Valle d'Aosta, in Italy.