The diacritics actually reflect pronunciation, so should be included, regardless of whether or not each writer used it. Adélaïde phonetically would be pronounced a-day-la-id (to render it into English similar phonetics, the ending E is silent), ie 4 syllable name. Without the diacritics, it would come out a-de-laid, 3 syllable name, which is obviously incorrect to anyone who speaks French.
In the Côté example of the other post, the earlier version of the name was Costé. The s disappeared and was replaced by the ô.
As you said, diacritics are haphazard in their usage in records, and the further back you go in time, the less we see them. Mostly because clergy often learned to write in Latin first, which language doesn't have such. They got introduced into written language with the invention of the printing press, as far as I remember from my earlier research on the subject. One also finds the tréma used on the letter U (ü) in names like Roüer for instance, to make sure the letter got read as U and not N. But that was another of these haphazard usages.
As a note, looking at her marriage record, there are 2 witnesses named, listed as friends, one of them named Michel Bois. Might she have been a foundling raised by the Bois family? A search in notarial records might clarify this, long shot to find, but not impossible. I've come across similar issue with another member, who actually found the notarial record involved then.
