If Russia's tactic is to cut and run.
Wouldn't it have been wise to create a base camp at the border and send wave after wave of small highly trained forces? This way, the Russians would meet them in the field filled with over confidence. Only to be met once more with another force the next day or so.
And if the russians use their patented cut and run tactic. The small french forces can easily keep themselves rationed and supplied as they rotating shifts with other companies, because clearly holding ground is a disadvantage. The Russians would slowly kill themselves as they kill off their supplies. And the french would continue to make ground towards Moscow, because they are constantly supplying and rationing. Holding no territories as clearly theres nothing of value to actually bother with.