It is an old fashioned term for straight woven tape - I have to say it's only the 1950's and earlier generations that know it by this term in England.
I occasionally get the older customer asking for it on the haberdashery stall and it always throws me because I can never remember if it is bias or straight tape.
backing that up, this article taken from a 1948 british newspaper lists bias and Paris binding for sale seperately:
another that lists both paris binding and twill stay tape, so it's not twill:
and this one describes it as a braid, which to me mean a finished edge on both sides, which bias binding wouldn't qualify as:
I found articles going back to the 1870s generally using the term paris binding, I think paris tape was used more in the 20thC.
a few more examples of early 20thC use:
( I wouldn't call bias binding 'strong tape' as it distorts when pulled...)
The more I look into it the more I wonder if Plaster of Paris Binding did not originate from Paris Plaster, but from Paris Binding being coated in plaster...