I wonder if the herb used in the duck rillette was salad burnet:
" With its clean, crisp cucumber flavor, salad burnet is surprising to those who try it for the first time, and appreciated the more it’s used in the kitchen. Introduced to Elizabethan England in the 16th century as an ornamental herb, the leaves were floated as a garnish in goblets of wine. "
I’ve had burnet used to flavor plain water (can’t remember the restaurant now) and it definitely has that cucumber-like taste and coolness.