Firstly, the forming of two ranks in 1813 does appear to be a one off 'ruse' rather than a tactical change.
As I have said, General Chambray wrote that the French infantry fought in 2-rank formation until the end of the war, i.e. until the end of the 1814 campaign. I am not sure that he is correct, but he did write that. Is there any source, which clearly says that the the French infantry fought in 3-rank formation in 1814?
The French were quite conservative really, and were still fighting as Frederick the Great had taught them.
I am sorry, I don't believe that Frederick the Great had taught the French to fight in skirmish order, to attack in battalion columns, etc.
Bardin describes a platoon (peleton) as having a minimum of 12 files. This is very small - I've not seen anything which says you should form two ranks if you fall below certain losses. Do not forget the platoons are equalised every day so loses would be evenly spread across a battalion (which is why you should not call them companies - a platoon can have men from different companies in it).
According to the Règlement concernant l’exercise et les manœuvres de l’infanterie du 1er août 1791, when a regiment, which is at the peacetime strength, is to carry out manoeuvres by battalion or by the whole regiment, the pelotons should be formed in 2 ranks (Titre premier, Formation d’un Régiment en ordre de Bataille). When a peloton is to perform the third, fourth, fifth, and sixth lessons of the Ecole de peloton, and there were less than 12 files in this peloton, the peloton should be formed in 2 ranks (Titre III, Ecole de peloton).
Bardin says the British were better at firing than the French because they practiced musketry more. He believed the French had the best musket, but they did not teach soldiers how to aim.
I am not sure that Bardin had enough information to judge whether the British practiced musketry more than the French did.