Fantastic exercise, I loved it!

Bonjour Blaise

"a washerwoman in Nice in the sixteenth century"

The story is a historical account of when "washerwoman" would have been the term used at that time.

Your proposal may be appropriate these days, but not at the time being related to in the sixteenth century.

This is why I don't feel able to agree with your point.

Bonne journée 

Jim 

Before checking, I would have said the same as Jim, but in fact it is wrong. 

For those who don’t want to read the detail below, Blaise is correct to raise the term “laundress” as it is both a better historical and modern alternative.

The term laundress dates back in written form in English to the mid-16th century, from French via launder,  somewhere around 1540-1555.  According  to most sources ‘ washerwoman’ was introduced significantly later in English.

AI Overview ( Safari response )

“ The word "laundress" originates from the Latin verb lavare ("to wash"), coming into English through Old French as lavandier (a washer) or lavandière (feminine) and Medieval Latin lavandaria ("things to be washed"). The English noun "launder" (a washer) was a contraction of this term, with "laundress" forming in the mid-16th century by adding the feminine suffix "-ess" to "launder". 

A breakdown of the word's etymology ( edited down to 2 points )

English development: 

1. The word "launder," referring to a washer of clothes, was a contraction of "lavender" and appeared in the mid-15th century.

2. Formation of "Laundress": In the mid-16th century, the word "laundress" was formed by adding the feminine suffix "-ess" (from French -esse) to the noun "launder" to denote a woman who performs the act of washing and ironing. “

And from Claude AI : 

“ In the 16th century:

Both terms would have been in use, but “laundress” was the more established and formal term by that period, having been in English since the 1300s. It appears in various 16th-century texts and documents.

“Washerwoman” was also used, though it had more of a plain, everyday quality as a native English compound. The term gained more prominence over subsequent centuries.

If you were writing historical fiction set in the 16th century, “laundress” would be the more period-appropriate choice, particularly in formal contexts or among educated speakers, though “washerwoman” wouldn’t be anachronistic either.​​​​​​​​​​​​​​​​ “

In contrast to ‘Claude’s ‘ comment though, the Oxford dictionary dates the first written use of ‘ washerwoman ‘ to the early 1600s, not the 16th century.

 https://www.oed.com/dictionary/laundress_n?tl=true 

https://www.oed.com/dictionary/washerwoman_n?tab=factsheet#14985045

https://www.etymonline.com/search?q=laundress