France seems to be the only area of the world for which "Our World in Data" has a complete dataset for forest cover for a long timespan -- it goes back to the year 1000 AD. Similar but less extensive data are available for a few other countries but, in most cases, the data cover only the past 30 years.
I can't say how reliable these data are, but the curve for France makes a lot of sense if compared with the historical record. Note how the late Medieval expansion corresponds to a decline in forest cover. The crusades (1095 -1291) see deforestation continue. Then, the whole economic system collapses: the crusaders go back to Europe to find the land devastated first by famines, and then by the Black Death. It is said that some 30% of the European population disappeared. Forests, then, had a chance to recover and attain levels similar to those of the early Medieval period.
Then, with the discovery of the New World, another cycle of expansion started. Population boomed, but the economic prosperity had to be paid, and in part was fueled, by another cycle of deforestation. It ended in mid 19th century with the start of a coal-based, industrial economy. Coal provided the same services as wood but at a lower cost, and that allowed the population to continue increasing without having to deforest the land. The trend continued with another cycle that started during the 20th century: the oil-based economy. The population rapidly shot upward, but deforestation didn't restart.
In the 21st century, we see the trend continuing, at least in rich countries such as Europe. Forests are still growing, while the population has now plateaued, and it is starting to decline. Globally, deforestation is continuing, but the reversal is clear in several countries (source)
So, there may be ground for optimism: forests may be regrowing as the world goes through its demographic transition. It is an especially welcome trend, now that the link between forest cover and rainfall is being recognized (see a recent paper in Nature).
But don't forget that the destruction of forests is always around the corner. During the Middle Ages, France had little more than ten million inhabitants, and yet it could raze its forests to the point of destroying its economy and causing some of the greatest famines in European history. We have been able to avoid this destiny, today, only because we have cheap energy from fossil fuels. Now that the fossil supply is dwindling, and with climate change looming as an even worse threat, we could see a new assault on forests, this time with the green label of "sustainable biofuels."
We need to understand that we need forests not because we can use wood to power our SUVs, but because they are part of the great planetary holobiont that connects everything to everything else. They generate the "biotic pump" mechanism that brings rain to the land (see this recent paper by Makarieva et al.). If we lose the forests, we lose rain. And if we lose rain, we lose everything.
