Combine clams and 3 cups water in a large stockpot; bring to a boil. Cover and cook 8 to 10 minutes or until clams open, discarding any unopened clams. Remove clams with a slotted spoon; set aside. Pour liquid through a wire-mesh strainer into a large container, discarding debris. Set clam liquid aside.
Melt butter in a Dutch oven over medium heat; add onion and celery, and saute 5 minutes or until tender. Whisk in flour; cook, whisking constantly, 1 minute. Gradually whisk in reserved clam liquid; cook over medium heat, whisking constantly, until thickened and bubbly. Add potatoes, reduce heat, and cook over low heat 15 to 20 minutes or until potatoes are tender.
Remove clams from shells, discarding shells. Peel membrane from clam necks and discard. Add clams, evaporated milk, and next 3 ingredients to potato mixture. Cook over medium-high heat until thoroughly heated. Top each serving with parsley, crumbled bacon, and a dash of paprika. Serve with French bread or crackers.