Frank,
Thiers is not really the best source. My understanding (sources Pelet, Arnold, Gill) is that the Saxon division under Dupas' command ascended the plateau alongside Lamarque's and performed creditably till the Austrian counter-attack drove the French back. At this point the troops were thrown together and there may have been 'friendly fire' incidents. Pelet just said: 'It has been claimed that the allied troops fired by mistake on Lamarque's opposite flank.' However, Bernadotte, who was supposed to be taking Wagram, did not come into action till too late, when the main assault had already failed.
So:
" during the fighting of the 5th July, 7-8 thousand among you pierced the centre of the enemy army and reached Deutsch-Wagram in spite of the efforts of 40 thousand men supported by 50 guns. You fought until midnight and bivouacked in the middle of the Austrian lines." Bernadotte
"The village of Deutsch Wagram was not in our power during the day of the 5th." Napoleon's response"
But : "The attack on Wagram took place, and our troops took possession of this village; but a column of Saxons and a column of French in the dark mistook each other for enemies and this operation failed." Napoleon's Bulletin.
Whatever the truth of the 'friendly fire' incident it seems to have been used by the Bulletin as an excuse for the village, which was not taken, not having been held.
regards,
Susan