Is there a way to smoothly move the player's camera position?

Maybe use TweenService.

local cam = game.Workspace.CurrentCamera
local mouse = game.Players.LocalPlayer:GetMouse()
local TweenService = game:GetService("TweenService")
local debounce = false
local aiming = false
local t= .3

local info = TweenInfo.new(t, Enum.EasingStyle.Linear,Enum.EasingDirection.In,0,false,0) --(time,easingStyle,EasingDirection,NumberOfRepeats,canRepeat,delay)

local Forward = { FieldOfView = 60  } -- change right side of equation to whatever
local Backward = {FieldOfView = 70 }

local zoomIn = TweenService:Create(cam,info,Forward) -- these create the tweens
local zoomOut = TweenService:Create(cam,info,Backward)

mouse.Button2Down:Connect(function() --change this to whatever makes the player aim
    if debounce == false then
        debounce = true
        zoomIn:Play() -- this plays the tween
    end
end)
mouse.Button2Up:Connect(function()
    if debounce == true then
        debounce = false
        zoomOut:Play()
    end
end)

Look up tweening if you want to learn more. Also, don't forget to mark this as the answer!