Place the softened cream cheese in a medium bowl. Add the crème fraîche, lemon zest, lemon juice, chopped dill, chives, salt, and pepper. Use a hand mixer or a whisk to beat the mixture until smooth and airy, about 1 minute—this makes the spread lighter and easier to smear.
Heat your broiler on high and position the oven rack about 6 inches from the element. Line a baking sheet with foil for easy cleanup.
Brush both sides of each bread slice lightly with olive oil. Arrange the slices in a single layer on the prepared sheet. Broil until the tops are golden and edges are crisp, about 2 to 3 minutes; flip and broil an additional 1 to 2 minutes so both sides have a touch of char. Watch closely to avoid burning.
Remove the toasts from the oven and let them rest on the sheet for 1 minute—this short rest keeps them crisp but not too hot to spread.
Spread a generous tablespoon (or to taste) of the whipped cream mixture onto each warm toast. The heat helps the spread loosen so it melds with the bread without becoming soggy.
Top each smeared toast with about 1 ounce of smoked salmon (folded or slightly piled), then scatter capers and a little extra dill over the top. Finish with a quick squeeze of lemon and a crack of black pepper to brighten the flavors.
Serve immediately while the toasts are still crisp. If making ahead, keep the spread chilled and assemble no more than 30 minutes before serving to preserve texture.