The 1970's seems a little bit early for the last person to have died, but that's often the period where it was clear in Western Europe that the old culture was gone, a process which arguably started with the end of the Second World War, or the that of the First World War, or the introduction of railroads and mass schooling and mass conscription in the 19th century, or even the agricultural revolution of the 18th century.

Let me just discuss farming for a moment. The agricultural revolution of the 18th and 19th centuries in many ways set up the industrial revolution which followed. Advances in agricultural science and technology meant more food could be produced from the same land more profitably using fewer people. You have things as simple crop rotation (this is often summarized as going from a three-field grain-oats/pulse-fallow rotation to a four-field wheat-turnips-barley-clover system, this not only decreases the amount of time each field is unproductive but also increases the nutrients available in the soil) to new technologies like steel plows, reapers, and eventually tractors. This let not only one farmer farm more land, but also opened up new land for productive agriculture. The John Deere self-scouring steel plow, for example, opened up the fertile areas of the American and Canadian prairies to massively more productive agriculture, and this exported surplus from both the New World and more efficient, increasingly large operations in Europe meant lower prices for small-hold farmers in Europe, which gradually pushed them off the land, especially as new opportunities opened up in cities. But for the most part, we see the shift from subsistence farming to wage labor for people in the country side ("proletarianization") and it's these wage-earning agricultural laborers who eventually migrate to the cities.

But this relatively plentiful, relatively cheap food, plus advances in hygiene and medicine, mean that even as agricultural labor as a percentage of total labor is declining in the 19th century (in much of Western Europe I imagine it's very roughly 50% in the 1880-1900 period), higher as you go further away from the heartlands of the Industrial Revolution, the rural population in numerical terms doesn't decline until later—one source I found says late 19th century for Western Europe, the 1920's for Central Europe and Scandinavia, 1930's for Eastern Europe. And this decline doesn't actually hurt agricultural output from these regions because of all the continuing productivity gains we see, such as tractorization.

The state increasingly crept in standardizing the country. In France, in 1870, probably less than half the country could speak French fluently (they spoke Occitan, Breton, Basque, Alsatian German, etc). By 1914, almost every was a fluent French speaker as railroads connecting isolate hamlets, the state conscripted more systematically, and above all we see a more national schooling system with a more national curriculum where almost every gets a primary education (exclusively in the national, standard, Parisian French). This national culture means it's also much easier for people to move nationally.

The upheavals of World War I and World War II expose country boys to the comforts and opportunities of the wider world, and many never move back home. Starting around World War I and increasing dramatically after World War II, it's also women who are leaving the countryside, and not just married to country boys moving to the city but on their own. Rural women in this period tended to be more formally educated than rural men because men typically left to work on the family farms whereas women were allowed to continue their education. In my grandmother's rural American family of 16 kids born in the 20's and 30's, all the daughters finished high school whereas I believe only the youngest two sons did. This opened up different sets of pink- and white-collar jobs in the city for women where they could support themselves financially. As the farm required less work, increasingly only the eldest sons would tend to the farm while younger sons were free to pursue their fortunes in the cities.

One of my favorite pieces of social science is by Pierre Bourdieu and is called The Bachelors' Ball. It has three parts, published in 1962, 1972 and 1989 respectively and gathered in a single volume only in 2008. Bourdieu is probably the most famous European sociologist of the Post-War era, but he began with this simple ethnography of a village in his home region of Bearn. These people could all speak French, but he was from the region—and introduced around by his father, a respected local farmer—and could speak to everyone in the local Bearnese dialect. The article published in 1962 is probably the most important, based on field work conducted I think in the late 1950's. Here, though, it's already clear to Bourdieu that the once prevailing economic system is doomed. He uses copious interviews and statistics to paint his picture, but the dominant image is of the "Bachelors' Ball". This is a tradition, here and elsewhere, where young single people got together and danced. And there was a growing population of older men who would never marry, who sat ominously together at the back of the ball, in his view hovering over and almost encroaching on the space of the younger people who would pair off and make better lives for themselves–somewhere else.

In the middle of the brightly lit dance-floor, a dozen couples are dancing to the latest tunes. They are mainly 'students' pupils at the high schools and colleges of the neighbouring towns. Standing at the edge of the dancing area, forming a dark mass, a group of older men look on in silence. All aged about thirty, they wear berets and unfashionably cut dark suits. As if drawn in by the temptation to join the dance, they move forward, narrowing the space left for the dancers. There they all are, all the bachelors.

The first-born sons used to have the good lot in life—they got the family farm. However, as economic conditions change, it was more beneficial economically (and more attractive to local women) to leave. The period from 1945-1975 is known in France as "les Trente Glorieuses", the Glorious Thirty [Years], as a time of booming economic growth almost across the board (Thomas Piketty and others argue that this was "catch up" period to make up for the slow growth of the Depression and the massive destruction of the Second World War). The first-born, however, could not take part in this highly urban economic growth, as they had to look after the farm because they had to look after the parents. They were left alone.

If they were in their 30's in the 1950's, they would only be in their 50's in the 1970's. Now, Bearn, tucked at the foot of the Pyrenees, is perhaps the most economically isolated corner of France, but I imagine most other rural areas were roughly in the same timescale—the Depression and the War ensured it. The last one was roughly in this period because of both rural and urban economic and social transformations that began more than two hundred years earlier but reach a crisis point in the Post-War era. You see more rapid rural depopulation, a shrinking agricultural workforce even as the productivity per (hect)acre continues to increase, and fewer farmer's sons for farmers to pass on the trade to. Of the sons that do exist, by that point, it becomes clear that the economic future lies largely elsewhere. Many of those who continue to live in the countryside no longer work in agriculture—they instead can drive their cars much further afield, so even when villages don't depopulate entirely, their economic base has fundamentally shifted away from pure agricultural dominance. What agriculture exists is now much more mechanized, much more financialized, much more complex than the farmers of generations past. But I'm not sure the last "real" farmers would have died in the 1970's. Even as late as 1970, 14% of the population of France worked in agriculture or a closely related sector. By 2020, it was 2.4%.

And it's also hard to downplay the significance of things like the sexual revolution of the 1960's (which I talk about a bit in this old answer), how much the tumultuous sixties reshaped social relations of all kinds, not just between men and women but between old and young, rural and urban, majority and minority. It felt, to many, like a rupture. And though many places experienced reactionary backlash in the 1970's, this was in part due to these social changes making their ways into all corners of the country.

Even though this is a relatively long answer, I feel like this is all still just scratching the surface of the truly titanic changes that entirely reshaped the economic and social structures of the world leading up to this period, such that people might tell you today that the last of the old breed, who remembers the old economic and social structures, died forty or fifty years ago.