Combine cornichons and liquid, onion, and peppers. Let relish sit 30 minutes, or refrigerate up to 2 hours.
Stir together mayonnaise and mustard, and refrigerate if not using immediately.
Slice baguettes horizontally but not all the way through so they open like a book (or a hot dog bun). Cut each baguette into pieces the same length as hot dogs.
Heat grill to medium-high, and brush grates with oil. Grill bread, cut side down, until just lightly charred, 1 to 2 minutes, then wrap in foil to keep warm. Grill hot dogs until lightly charred on all sides and warmed through, 5 to 6 minutes.
Spread inside of bread with mayonnaise mixture, and place a hot dog in each. Spoon relish over top.