One of Mr. Smith's links https://books.google.com/books?id=XihIAQAAMAAJ&pg=PA337 Bulletin of 24 octobre 1813
To me this bulletin tells the story. Everything was fine and working according to N.'s plan and the French Army is victorious right up until. . . Kaboom!
According to the bulletin the numbers lost was 12,000 men and 200 carts so most of the army still made it across the bridge.
If the bridge was blown at just the right time -after all of the army got across safely- there would be no talk about needing temporary bridges.