Latin mappa reached Middle English nape through Anglo-French. Nape meant tablecloth and supplied nappekin, behind napkin.
Anglo-French mediation is compressed between mappa and Middle English nape; the two English stages remain separate.
Sources
- Merriam-Webster: napkin
The formation and borrowing route are explicit; the child entry names the apron and map connections.
- University of Michigan historical dictionaries · MED29074
Meanings of the older forms on the word path.