In a large nonstick saucepan, melt butter. Add shallots and cook, stirring occasionally, until tender but not browned, about 5 minutes.
Add wine, tarragon and vinegar; reduce heat to low and simmer 3 minutes.
In a large bowl, combine Gruyère and Cantalet cheeses. Add cornstarch and toss until well coated.
Add cheese to saucepan a handful at a time, stirring after each addition until melted.
Cook over medium-low heat, stirring constantly, until smooth and thickened, about 10 minutes. Pour into fondue pot set over a flame and serve with dippers.