I do not believe the version of "par . . . " you suggest is always the case. This is because colonne serrée can mean a row of columns.

BH: Ralph: Okay, then 'par --' can refer to both the frontage of a battalion column and the formation of several battalions. I can see how the change from nine to six company battalions could throw the entire technical use of terms into linguistical confusion, and make attack columns very awkward with the necessity of having a one peloton front, stacking half-companies to create the new 'five company' attack column on a peloton front instead of the old 'eight companies' on a division front.

Ralph wrote:
Ney wrote about "la colonnes serrées par régiment" he did not mean a regimental fronts for each column. Rather he means a series of columns each of said columns containing a regiment with one battalion in front and a second battalion behind it (odd in front with even behind or even in front with odd behind).

See NEY MÉMOIRES – VOL 2, PAGE 296 uses both "colonne serrée par régiment" and "colonnes serrées par régiment" yet the text makes clear what he means:

BH: Actually, it isn't clear to me. He speaks of four regiments, two battalions each I am supposing. He says: form two lines, place the odd battalions in the first one and the even battalions in the second, THEN form closed column by regiment. The rest of the description is how the battalions of the two lines will form and space themselves based on the 4th or 1st division of the battalion before it depending on whether odd or even battalions are in the first line.

So, the question is: what would the formation will look like? If the first and second battalions for ONE column, then you don't have two lines. IF the the second and forth Regiments are assumed to make up the second line of paired battalions, four regimental columns in all with two in the first line and two in the second, then his description at the end doesn't make sense to me--at least:
"Mais si le commandant-général voulait que les bataillons pairs fussent à la première , et les impairs à la seconde ligne, les colonnes serrées par régiment se formeraient sur la 1re division des bataillons pairs , la gauche en tête."

Is Ney describing one line of four regiments or two lines of two regiments? IF 'la colonne serrée par régiment ' refers to a regimental column, there is no need to speak of 'two lines' with odd in the first, even in the second. Why bother with that description? Why not simply say four regiments in one or two lines of 'la colonne serrée par régiment,' odd or even battalions in front?

It isn't clear to me. Certainly technical French from 1800 can be opaque to me, a beginner in the language.

Best Regards,
Bill H.

"Les quatre régimens étant déployés et le commandant-général voulant former de suite deux lignes, placer les bataillons impairs à la première et les bataillons pairs à la seconde , il formera la colonne serrée par régiment, la droite en tète ; sur la 4e division des bataillons impairs , il rapprochera les masses à distance de bataillon sur le 2e régiment , et fera ensuite déployer sur la division du drapeau de chaque bataillon. Mais si le commandant-général voulait que les bataillons pairs fussent à la première , et les impairs à la seconde ligne, les colonnes serrées par régiment se formeraient sur la 1re division des bataillons pairs , la gauche en tête ; les masses seraient rapprochées à distance de bataillon sur le 3e régiment , et le déploiement aurait également lieu sur la division du drapeau de chaque bataillon."