It seems somewhat out of linguistic character for them to use the English-"shrink"-based portmanteau, but hopefully there's a universal commonality (especially coupled with the hashtag format) that makes this move more effective.
[1] https://www.encyclopedia.com/humanities/encyclopedias-almana...
They especially love -ing endings and will stick them on when it wouldn’t make sense in English. Ever notice the French for shampoo on also-sold-in-Canada shampoo bottles in the US? Shampooing. As a noun. And that’s not some Quebecois thing, it’s French French. Maybe they also like the “sh-“, and that made “shrinkflation” appealing.
They also use “parking”. “Le parking”. As in parking lot. Again, as a noun.
[edit] Shampooing is said “sham-pwan”, more or less, hitting the “n” rather softly, but parking is spoken almost the same as in English.
(Tuxedo and blow dry, respectively.)