Is there a historical reason for the fact that Chalmers university uses a French motto and not a Swedish one?
Avancez! was the personal motto of William Chalmers, a member of the Swedish East India Company, who left about half of his personal wealth to supply for a school which eventually became the current university (the other half went to Sahlgrenska sjukhuset, a hospital founded by one of his colleagues). The school has copied his motto.
French used to have a status as working language for international institutions, somewhat like English today (or Latin in the past for Catholic Europe). This was the case around the time of the founding of Chalmers University of Technology (1829). It is not surprising if some universities during that time used a French motto. Today there are also universities and other institutions in non English-speaking countries that uses English motto, for example Erasmus University.
French was the language of diplomacy from the 17th century until the mid-20th century, and is still a working language of some international institutions. In the international sporting world French is still the lingua franca as the International Olympic Committee and FIFA use French. It was also the lingua franca of European literature in the 18th century. French is still seen on documents ranging from passports to airmail letters.
"Avancez" was the "motto" of the Scottish & British noble family (at the time.) known as Chalmers of Gadgirth. Chalmers (and the surnames Chambers & Chamberlain), came from their family's beginnings as the ancestors of French nobles who were Chamberlain's to King David the 1st, Malcolm the 4th and James the 3rd. At the time, they called themselves "De Camera" and "Camerarius". Herbertus was the first on record. Herbertus, Camerarius Regis Scotiae (Chamberlain to the King of Scots). The name De Camera then morphed into Chalmer and Chamber. And then finally, Chalmers and Chambers. Some Chalmers families broke off and went on to use the motto - "Spero", which means "Hope". I believe William Chalmers, who the university is named after, was from the Chalmers of Gadgirth family. So, he kept the original family motto of "Avancez", which is now the motto of the university founded in his honour.