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 de 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 de 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.