You really messed up my map
But wait... Your German army deployment is almost identical to OTL 'Aufmarsch II west', except that the three armies invading Belgium are missing (see
German Army order of battle (1914)). This setup is not to be expected in a defensive strategy in the west. In OTL, a strong defense of Lorraine was not a priority, as the French armies would be distracted anyway by the German advance in northern France. According to
Plan XVII, the main French force attacks between Metz and the Vosges. The German defense plan is to attack and encircle the French armies invading Lorraine from the directions of Metz and Strasbourg. This is clearly explained in
this post from @Athelstane.
Whoops, you are right. I had this same file, but I opened the historical pdf instead of the one I was supposed to be looking at. However, this actually spreads out the German defenders even more. The historical 6th army is now responsible for the Metz fortress area (second army on your map), which may dilute some of their landwehr units or even a reserve corps. This probably won't have any real effect on the battle. The historical 5th army (3rd XXXX on your map), instead of being concentrated northwest of Metz, is spread out now and would also cover the Luxembourg front. This means that area will have a more "normal" initial German troop density, probably allowing the French to actually take more territory north of Metz and in Luxembourg before they are stopped due to their initially greater relative combat power here (though certainly only a bit more than in my map).
The German 7th army, instead of being slotted into the line in the north on my map would probably move it's HQ a little west of Strassbourg, with its units being generally spread out to solidify the front (maybe a couple reserve corps still guarding the Belgian border). This would take some time, but it would also take time for the French 4th and 5th armies to move into position, together with the German ersatz divisions. This would stabilize the front after the initial French advances, though both sides would still suffer greatly.
The plan Hermann von Staabs devised after WW1 looks different again, with only 3 armies in the west between Cologne and Strasbourg, and 5 armies in the east. A little googling brought me to
this interesting post by @NoMommsen in the thread '
WI: Reverse Schlieffen Plan', in which this plan is explained (including maps).
However, there were more German veterans who reconsidered the chosen strategy after WW1, such as Ludwig Beck. His plan is described in this interesting thread: '
FYI : about Ludwig Beck on "East First 1914"'. When making my maps I was inspired by Beck's plan. With this plan, three German armies are available from Metz to Strasbourg. This makes it possible to encircle the French armies IMO, provided Joffre is of course reckless enough to advance far enough towards Saarbrücken.
This is a very different scenario. It seems on first glance to be a terrible strategic idea by the Germans based on their thinking in 1914, since there still isn't enough force for a major advance in the east, and they only have somewhat more combat power in the west on a narrow front. In the east, the moderately increased German force would likely make the Russians more cautious, avoiding Tannenburg, though the Germans could still probably advance by the end of the year and might even capture Warsaw. In the West, the exact outcome depends on the situation.
If the Germans advanced, they would run into the French in a meeting engagement. They would still win, but the strength of the defense together with mobilization of French reserved would probably stabilize the front close to where you predicted above.
If the Germans waited to defense, the ultimate outcome would be similar to the above, but the initially stronger German counterattack would push the front back a little more, keeping the fighting solidly in French territory as winter approached. The German front line in Lorraine would likely be advanced compared to the historical level, though the lack of an attack through Belgium would mean that the iron northeast of Verdun would still be in French hands.
However, you seem to be imagining a situation where the Germans are quite clever and try to suck the French deep into Lorraine before counterattacking and trying to create a cauldron battle. This seems less likely to me, since both generals and politicians are notoriously difficult about conducting withdrawals when there is not a great strategic or operational need. However, it is certainly an interesting possibility. The French here would be overextended, and they would face many more Germans than in the historical battle in the areas (and much more than the von Stabbs plan discussed above). It seems quite likely that the Germans could score a major victory, leaving the French in headlong retreat. The line might not stabilize until deeper in France. Perhaps Nancy would even become the "Verdun" of this timeline. The need for French reinforcements in this area may also allow the Germans to take more of the iron mines northeast of Verdun, though probably still not quite at the historical level,a gain, due to lack of advance from another direction and the relatively more intact French forces in the area.
However, I really do not believe that the French would have any real chance to get any of their division or larger size units surrounded, even in this favorable scenario. This sort of thing only happened twice in WWI to my knowledge, at Tannenburg and Kut. In both the scenarios, troop density was low, and armies were operating with open flanks. Here, even with greater German combat power, the French troop density is high, easily enough to cover their flanks during an advance (and clearly so high for both sides that they would never leave the flanks uncovered). The French would have reserves, and their troop quality was good, with troops in good condition. As noted above, they could easily suffer a Gorlice-Tarnow like defeat if the Germans conduct themselves well and the French poorly, with many prisoners and loss of heavy equipment. This is very different than loss of entire large units, though, which is probably just not realistically possible in this situation.
Of course, in the long run, this sort of plan could still be favorable to the Germans, even if it didn't seem that way in 1914. By keeping the west in stalemate, conducting a limited but successful campaign against Russia (so as not to make it a war of national defense, like what might happen in the von Stabbs plan - or make the Briotish fear that the balance of powerr may be severely disrupted), avoiding anything even remotely resembling provocation at sea, avoiding getting the Ottomans involved, and focusing the only really intense attack on Serbia, the Central Powers could perhaps acheive a limited but solid victory in 1915 if these measures are successful at keeping Britain out of the war. Again, though, it seems less likely that a great power in a major war would follow such a restrained path.
As for the battle north of Metz. This is a hilly terrain in which the French will not get far. Yes, the iron industry is in the middle of a war zone and will be badly damaged and useless to both Germany and France. As I have said before in this thread, French industry in the Orne valley is within range of the German fortress artillery. However, taking possession of the iron ore basin could turn into a strategic battle. I give Germany the best chances, given their heavier howitzers and mortars...
All industry and mines very close to the front would certainly be closed. Regardless of which of the above scenarios is used, though, the French are still "ahead in the iron game" compared to the historical level (even in the second scenario where the front lines end up in France).