As for champagne, it's my understanding that legally, you cannot advertise it as such unless the grapes come specifically from the Champagne region of France. So, it would be false advertising, at the very least, to call it that if the grapes are sourced elsewhere. It's kind of like calling all copy machines a Xerox even if it's not a Xerox brand.
Yes, the grapes don't come out of the ground all sparkling and bubbling. If you find some that are, don't eat them! They are fermenting on their own.
The Champagne region developed the sparking fermentation
process some 4 centuries ago. So, they have a protected trademark or what ever it's called over there. Also, the
way their grapes grow is truly different than if you took vines from the same grapes and grew them elsewhere, say California.
I remember watching some movie or TV show that explained the way the warm, moist air comes up from the Mediterranean, versus the cold air coming from the North is what accounts for the Champagne region's climate, temperature, weather and soil. Then need BOTH the warm & cold airs.
California doesn't have those same conditions. So, even if one took some vines from Champagne and grew them in California, the harvest would be totally different, and it would affect the overall taste. So, in California and other places, they make
sparking wines. But, only in the Champagne region with Champagne grown, cultivated, harvested and aged in Champagne can be it called a true champagne.
Back to being PDO, I remember watching Stanley Tucci's wonderful food series,
Searching For Italy, 
where he went around to different regions in Italy and talked to generations old farmers, ranchers, cheese, meat and sausage makers. I think wine makers too. They said the same thing as the French winemakers. Each region is known for different types of foods than each other. The wind & weather coming off the Mediterranean versus the cold winds from the Alps created types of soil, terrain, shrubbery & grasses in different regions that the animals munch on. The animals or the milk (cheeses) they produce truly taste different according to what they
eat.
I forget which episode it was, but one time, it was told that some farmers were smuggling in fake pigs(?) that weren't authentic to the area. It might have been in Parma(?) They were much, much cheaper to smuggle in, grow and sell the meat of.
However, it was obvious from the lack of marbling, lack of rich color, lack of fat, and mostly lack of FLAVOR that what they produced wasn't authentic prosciutto ham. Although they were charging the same price as for the authentic PDO meat.
Stanley was given a plate of each and he could tell the difference right away. So could we viewers. We didn't have to taste it the way Stanley did. The comparison was so obvious. It was like holding up a dollar store cheese curl (looking more like a styrofoam packing peanut) next to an authentic Cheetos brand cheese curl with all it's orangey cheesey goodness.
The EU's Protected Designation of Origin government officials could tell right away too. They rounded up all the suspect faux pigs (and farmers) and DNA tested the pigs. Since all the various animals of a PDO region are all supposed to have lineage tracing back centuries, that means each type of animal has been inbred and thus have similar DNA, and it is only found within that region.
Sure enough, the faux pigs had different DNA. The non-PDO meats were pulled and the farmers went to prison or were fined immensely.
Don't mess with the EU's Protected Designation of Origin government officials.
