In a food processor, add the smoked salmon along with the mayonnaise and some pepper. Pulse just until the salmon is broken up into slightly smaller pieces. Do not overmix.
Place the mixture into a bowl and combine with the raw salmon and creme fraiche or sour cream. You may add more or less depending on how creamy you like it. Add the shallot, lemon zest and juice and half the chives. Season with pepper; the mixture will likely not need salt due to the smoked salmon.
Transfer the mixture to a shallow wide bowl and cover with the remaining chives. Serve with crostini.