Why did letters in French start halfway down the page?

Question

      The structure of a page communicates much of how we understand a text (Mountford 1990). Material at the top written in larger type, often centred, is usually a title. A number in the upper or lower (occasionally the outer) margin is a page number (note how odd it would be to have the page number in the middle of the inside margin). A small raised number in the text is a footnote reference. At the beginning of a book, a list of terms followed by numbers is likely a table of contents; at the end of a book, a list of terms followed by numbers is likely an index. The table of contents and the index are sometimes labeled as such, but even without the labels, we recognize them by their position in the book. Correspondence has a fairly fixed format: date, salutation, text, closing signature. Letters in French used to start halfway down the page. [emphasis mine] In German letters, the salutation ends in an exclamation mark; in English, a comma or colon is used, with a sociolinguistic difference of formality.

Henry Rogers, Writing Systems (2004), pages 15-16.

Answer 1

As iNyar commented, this space is intended to show the sender's deference to the recipient. The larger the gap, the more respect was shown.

Here is an excerpt from Modeles de Lettres Sur Differents Sujets, Choisis Dans Les Meilleurs Auteurs Epistolaires by Louis Philippon de La Madelaine, 1761

That reads:

    Entre cette qualification de la personne et le commencement de la Lettre, vous laissez un intervalle plus ou moins grand, selon le respect que vous lui devez; et c'est là ce que l'on appelle communément « donner la ligne ».

i.e.

    Between this qualification of the person and the beginning of the letter, you leave a greater or lesser interval, according to the respect you owe him; and this is what is commonly called donner la ligne (to give some line).

I don't have any source for the reasoning behind it, but my guess is that this space represents the distance you put between the person you are writing to and yourself, like at court, you didn't get too close to someone in high rank.

An expression that recently came back into fashion names it: social distancing.