To mods : Im not a historian but I did work as a journalist, researcher and field producer on a documentary on the Zone Rouge, the restricted area which used to cover most of WW1 frontlines, and I interviewed the Démineurs (bomb removal specialists in charge of explosives clearance since 1945) working there daily, as well as Interior Ministry officials and their in-house historian, and many local residents in the Moselle county in Eastern France. The following information is from Démineurs Central Office internal documents and archives they provided and the interviews I did with them, I have tried to explain as best I could (although I'm not sure this follows the appropriate method and tone for this subreddit) and I also included figures when available.

Due to the immense area the frontline covered as well as the inconceivable amount metal debris, traps laid and bombs dropped over a 4 year period, a significant portion of which haven't detonated on impact, the authorities never could clear the whole frontlines of WWI. Much of the land still carries the deformities from this quite recent and very violent historical period. Although time has done a good job of hiding some of the more visible aspects of the conflict if you walk around the North and East of France you can still see to this day remnants of trenches, fortifications, shell impacts, and unfortunately a vast amount of unexploded ordnance laying either in the woodland surface or in the top layers of the soil.

At the end of WWI the french government created a minesweeping service to clear the top layer of unexploded shells, and starting in 1920 this was replaced by private contractors to clear the frontlines and recover all the metal debris and unexploded bombs (the Interior Ministry calls it REG for "Restes Explosifs de Guerres" or Explosive War Leftovers). The government circled the "polluted area" on the map with a red marker and forbade access to it. It was thereafter known as the Zone Rouge, or Red Zone. Most previous municipalities had been reduced to rubble and residents had left the area during the fighting anyway, but the idea was that this area stretching close to two hunded kilometers following roughly the France Belgium border (total area is 33.000 square kilometers or 30 times the size of New York City), was too unsafe for civilian use and hence declared out of bounds. Part of the German reparations included replanting trees in that area hence the Schwarz Wald pine tree forests which cover a lot of Zone Rouge still today and have helped in reshaping the land after the conflict. Over time the plan was that local municipalities and private owners would be able to recover land for agricultural use as was the case before the war. Private contractors were given a lease on the land they were to "de-pollute" and expected to pay a fee to the state per kilogram for the metal they gathered, the whole operation being supervised by a military command. After the 1929 crisis and the fall in metal prices this was no longer profitable and the state decided to both let contractors sell all the metal they found with no fee and even pay them for this work. Clearing the area, however, proved a huge task with a steep human cost as many workers died from exploding leftover shells doing so. One billion shells of all calibres (or 15 million tons of metal) were fired over french soil during WWI according to Interior Ministry estimates and roughly 25% never exploded (including 6% containing combat gas), which left over 250 million deadly explosives in the ground in the region now found accross the counties of Meurthe-et-Moselle, Moselle, Ardennes, Meuse, Marne, Aisne, Somme, Oise and Nord. I dont have an estimate of how much material was collected, shells or otherwise, after WWI. Internal documents from the Service du Déminage state that during the interwar period "the [Explosive War Leftovers] were extracted at surface levels, in the absence of detection equipment. Picking to a depth of 10 to 20 centimeters was considered, but the second conflict put an end to these activities."

After WWII the authorities also had to deal with close to 600.000 tons (source is Interior Ministry as well) of Allied bombs dropped both in that same area and all over the country as part of efforts to liberate France from German occupation. The government decided the task of recovering unexploded shells should be given to a centralised civilian force and in 1945 they created the Service du Dèminage or simply Démineurs (which translates to "Minesweepers"). By then some of the areas which used to be part of Zone Rouge had already returned to being farmland or forests, although not necessarily because they had completely been cleared from debris and shells but also because of locals' eagerness to use the land (some locals also mention a bit of corruption at the local level as farmers tried to get access to more arable land). What's sure is that much farmland in the area, as well as land which was later developed and urbanized, still today contains unexploded ordnance, which are found daily by farmers and residents as soil is moved around. The Démineurs deal with this on a daily basis, at a risk, as specialists die every now and then from accidents while handling 100-year old explosive and gas shells (the latter being especially prone to leaks and/or detonation). Figures from the 40s and 50s from the Démineurs Service mention dozens of civilian deaths every year and at least 1 démineur deaths every year and up to 391 for one year in 1945 (that last figure most likely relates to german POWs being used as live bait to trigger mines at the end of the war, but thats another story).

So as to your specific question: my understanding is that the project of clearing the No Man's Land area for civilian use was so vast that the priority was not so much to remove trenches and military infrastructure rather than the millions of tons of metal poured onto the battlefield, including deadly weapons (mostly unexploded shells). In fact some of these trenches and fortifications are visible still today in many areas which haven't been reclaimed by farmers, both in touristic sites open for visit and others simply in random forested areas. Over time the land that has been reclaimed by farmers just looks like farmland and the forests just look like forests, at least at first glance, but they carry the scars of battle still : farmers get their tractors and mechanical plows broken every year from century-old metal debris coming back to the surface and sometimes even exploding shells and they all have stories relating to such discoveries. The forests are still quite dangerous and there are signs that warn not to stray off paths as unexploded ordnance is found daily, even in parts were civilian access has been restored. The process of clearing the land continues up to this day, and at a rate of around 400 tons of shells cleared every year the Démineurs estimate that WWI ordnance will take another two to seven centuries to clear completely. Again, they also have to deal with leftover WWII aerial bombs and ordnance, as well as other duties such as handling high risk explosive chemicals, bomb threat assessment and lately also terrorism-related explosive security. The Démineurs like to remind that beyond the two large conflicts of the 20th century they are still recovering debris and sometimes shells from the 1870 war between Germany and France in that area. Hope this is of interest.