I go two ways with a tarragon vinaigrette. One way is to use tarragon mustard instead of plain Dijon mustard as the emulsifier. The other is to use a tarragon infused vinegar and a standard 3:1 oil to vinegar ratio. Both methods work well
When I have tarragon in the garden, I like to chop it fine and add it to my favorite vinaigrette recipe (with regular Dijon as the emulsifier). Otherwise, I do what Chris recommends first.
I made one last night with some good quality mayo, fresh black pepper, salt, a good helping of fresh tarragon from my garden and the juice of half a lemon. Used this dressing on a cauliflower, broccoli salad with onion and crumbled local bacon...and some fresh cherry tomatoes from my garden.
Tarragon vinaigrette is a big fave at Chez Julia. I've made it both with tarragon mustard and with fresh tarragon and regular Dijon. It's good both ways!