The route goes through Late Latin mussirio, Anglo-French musseron and Middle English musheron.
Anglo-French musherum is an alternative to musseron. The Latin stem mussirion- is not another independent chronological stage.
Sources
- Merriam-Webster: mushroom
Noun Word History supplies the selected route and alternative forms.
- University of Michigan historical dictionaries · MED28961
Meanings of the older forms on the word path.
- Centre National de Ressources Textuelles et Lexicales · mousseron
Meanings of the older forms on the word path.
- Anglo-Norman Dictionary · musseron 2
Meanings of the older forms on the word path.