In a medium bowl, toss radish and shallot together. To a small saucepan, add vinegar, sugar, fennel and salt; bring to a boil. Reduce heat and simmer for a few minutes; cool.
Spoon the radish/shallot mixture into a 2-cup (500-mL) Mason jar, then fill the jar with the liquid. Top with sprig of tarragon. Seal and refrigerate for one day before serving.
These pickles will keep in the refrigerator for 3-4 weeks. Makes one 2-cup (500-mL) jar.