The French would deploy 3 of their active armies (4th, 2nd, and the left wing of 1st, West to East) between the Moselle and the Vosges attacking North toward Lorraine as well as part of the 3rd Army, which would invest/screen Metz and cover 4th Army's left wing with 3 corps. In total that's 28 active divisions between Metz and the Bruche, with another 9 reserve divisions in the rear. 5th Army would attack between Metz and the Luxembourg border along with part of 3rd army, 12 divisions, only entering Luxembourg if the Germans did first. Plan XVII below for reference:
Germany would deploy 4 armies (1st - 4th) in the East and 3 (5th-7th) in the West. 34 active/reserve divisions would deploy in the West (17 Corps) while 43 would deploy East (21 Corps + 1 Division). There would also be 6 Ersatz divisions floating about which would probably go West, so as OP says you'd have an almost 50-50 even split of 43 divisions East, 40 divisions West.
The German initial mobilization would be 5th Army with 5 corps from Metz to the Belgian border, 6th and 7th Armies with 10 Corps between Metz and Strasbourg, and 2 separate Corps in Upper Alsace around Mulhouse to await the arrival of the Italian Army. The German intention was to remain flexible and concentrate the majority of its forces against the main French blow. Luxembourg would be invaded with cavalry and VII Corps would occupy the Moselle, Our, and Sur bridges leading into the country.
Under these circumstances, the main fighting will occur between the German 6th/7th Armies and the French 4th/2nd/1st Armies between Metz and Strasbourg. Lets not forget that, IOTL, the German victory in Lorraine was achieved with a localized numerical superiority (7-8 German Corps vs 6 French) because Joffre had already shifted his main point of effort to the Ardennes. With the equally hefty material strength committed to both parties, it seems likely the frontline will devolve at the very least into a back-and-forth push as it did IOTL, with the Germans withdrawing across their border to better defensive positions even if they achieve initial local success rather than overstretching themselves against superior numbers.
Moltke hoped for a full on battle of destruction by enveloping French forces between Metz and Strasburg. This seems unlikely to me, simply because of the density of forces involved (37 French divisions and at least 20 German) and the French 3rd Army providing support on the 4th Army's left. 1st Army's right seems like a natural place to deliver a painful defeat, but the French left doesn't offer similar opportunities.
From Metz to the Belgian border, the Metz-Thionville fortress complex will halt French forces along the Moselle while 5th Army is counterattacked by a smaller German force in Luxembourg. With the French able to rally on their fortresses in the Longwy region and possessing superior numbers, a German pursuit from Luxembourg or attack across the Moselle seems unlikely with the main battle unfolding further East.
By the end of August the French Army will have cleared out most of its riff-raff commanders and will have superior numbers (67+ divisions to 40) across the front, more than enough to push the Germans back across the border and perhaps even occupy parts of Upper Alsace and Luxembourg. Eventually shell shortages by the beginning of October as well as the fortress complex of Metz-Thionville will put an end to the fighting, at which point France will have to reorganize its army and industry for a new offensive.
We should recall that while the French Army's performance wasn't its best in August 1914 IOTL, its defeats occurred in circumstances where it was outnumbered operationally and strategically outmaneuvered. A few weeks later it inflicted a major defeat on the German Army and then fought it to a standstill from the Somme to the Channel. A battle in Lorraine would allow the French army to fight exactly as planned and have clear operational superiority in numbers. I think a strategic stalemate on the German side of the border is most likely, but it would be unrealistic to discount the possibility of a major French success which attracts additional German reserves.