Short answers, pulled from the story.
Gallo-Romance is a branch of the Romance languages that includes, in its narrowest definition, the langues d'oil and Franco-Provencal. Broader definitions also encompass Occitano-Romance, Rhaeto-Romance, and Gallo-Italic languages. The family spans northern France, Belgium, Switzerland, and parts of Italy and Spain.
The Oaths of Strasbourg were sworn in 842 AD and are among the oldest surviving documents written in vernacular Romance languages. Old Gallo-Romance was one of the two languages used to record the oaths, making the text a key early document in the history of the Gallo-Romance family.
The langues d'oil include French, Orleanais, Gallo, Angevin, Tourangeau, Saintongeais, Poitevin, Bourguignon, Picard, Walloon, Lorrain, and Norman. This group forms the core of the narrowest definition of Gallo-Romance.
Franco-Provencal is a language group spoken in east-central France, western Switzerland, and the Aosta Valley of northwestern Italy. Once thought to be a dialect of either langue d'oil or Occitan, it is now recognized as a separate group with its own dialects, many of which have little mutual intelligibility. It shares features with both French and Occitan.
The Von Wartburg line is the historical border between the northern and southern varieties of Gallo-Romance languages. It marks the geographic and linguistic divide between the langue d'oil zone in the north and the southern Gallo-Romance languages such as Occitan.
Gallo-Romance languages are considered the most innovative because they underwent the most extreme phonological changes of any Romance branch. Northern France, the medieval home of the langue d'oil, was the epicentre of these changes, which included the early loss of final vowels, heavy reduction of unstressed interior vowels, and extreme lenition of consonants. French, for example, reduced five distinct Latin words to a single identical pronunciation.