Place fennel into a sealable container with cinnamon sticks. Cover with white wine and set aside for 30 minutes to soak.
Fresh Nova Scotia Arctic Charr has a natural sliminess on the outside. There is no need to scale this fish, simply rinse charr inside and out with cold water to remove any sliminess and blood. Pat dry with paper toweling and place fish into a large sealable container. Pour wine over fish, turning to coat. Cover and refrigerate for 20 minutes, turning once, allowing charr to marinate.
Preheat grill to medium heat, about 350 degrees F.
Remove charr from fridge. Remove 2 cinnamon sticks and 8-10 pieces of fennel from the wine, and divide evenly into the belly of each fish. Add sliced shallot, a sprig of tarragon and set aside.
Place cinnamon sticks directly onto grill to form a bed. (To allow for easy removal, you may place cinnamon sticks onto a perforated metal pizza tray, or grill tray.) Top cinnamon sticks and fennel with remaining tarragon. Remove charr from wine, discard wine, and place stuffed arctic charr onto cinnamon stick bed. Season outside of fish with sea salt and freshly ground black pepper to taste.
Close lid of grill and allow to fish to bake on the cinnamon sticks for 30 minutes, turning once, and checking occasionally that cinnamon sticks are not on fire. Fish is fully cooked when firm to the touch, and flesh along the backbone flakes easily when pierced. If cinnamon sticks ignite, using a spray bottle, carefully spray flames with water.
Remove charr from grill, and transfer directly onto a serving platter. Remove cinnamon stick from belly. Drizzle with fresh squeezed lemon juice, a splash of spiced rum and serve immediately.