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"An early summer offensive failed" By which side? France. Done
"subsequently, both French armies held significant footholds on the east bank of the Rhine." Should "subsequently" be 'consequently'? Done
"was the actual cause of the French failure" Suggestion only, "actual" -> 'main'? Done
"From 1793 to 1794, French success varied." Reads a little oddly. Perhaps "success" -> 'fortunes'? Done
"The formation of the new demi-brigades, units combined the old military units with new revolutionary formations" This isn't a sentence. Done
"The losses of this revolutionized army early in the Rhine Campaign of 1795 disappointed the French public and the French government." I am not sure about this, but does something which arose out of the events of the campaign belong in Background? reworded
"the state that controlled its crossings controlled the river and access into the territories on either side" I am not sure what "the river" adds to this. Done
"For the French, the more German territory they could control, control of the Upper Danube would give the them a reliable approach to Vienna." The two clauses of this seem disjointed. Is something missing? Done
"an army could also use the river's flow to approach the Austrian capital" How? (Assuming they are marching and not swimming.) rafts and boats
Yes. I know that. A reader wouldn't.
To me, it looks as if the material under "Plans for 1795" down to cite 12, would fit better under "Geography". Done
French Directory is duplinked. links to a specific portion of the article.
"increasingly worthless" If something is worthless, how can it become increasingly so? Done
"The Coalition garrison of 9,600" I know that you have already introduced the War of the First Coalition, but I think that the sudden switch from "Habsburg" to "Coalition" is likely to confuse readers. explained coalition above
"engaged 12,000 Republican French soldiers" Is "Republican" necessary? I think so...there were a lot of French soldiers in the emigre army too.
In which case make the latter clear?
"For example, in its prompt capitulation of Mannheim, the Bavarian garrison had surrendered all supplies, horses, armaments, and weaponry, an action that further confirmed to the Habsburg commanders that their allies were not reliable." This is under "Subsequent plans", which seems a little late in the article.
"They placed Archduke Charles, Duke of Teschen, the emperor's brother" Suggestion only, delete "Duke of Teschen". he is referred toboth ways.
True. Royalty usually have a long list of formal titles. It is customary to only refer to them by the most senior. (The Duke of Teschen bit is only in his Wikipedia article as a disambiguator.)
"and arguably the best of the Habsburg generals" "arguably" - word to watch; according to whom? according to the cite. And most modern historians. and most of the people fighting him. :)
Personally I completely agree. But Wikipedia doesn't care about my opinion.
"Charles had half the number of troops" half of what? You don't give the comparatator. Done
I would have thought that cadre was standard English and didn't need to be in italics.
"If there has been a previous A-Class nomination of the article, before re-nominating the article the old nomination page must be moved to Wikipedia:WikiProject Military history/Assessment/Name of nominated article/archive1 to make way for the new nomination page." Did you do this?