My sprint script not changing animation! How to fix?

This should fix it, but you have to change both of your animation's priorities to "Movement" and toggle looping for both of the animations that should fix everything.

local player = game.Players.LocalPlayer--The local player variable
local Camera = workspace.Camera--The camera variable
local NormalSpeed = 16--The normal speed variable
local SprintSpeed = 33--The sprint speed variable
local UserInputService = game:GetService("UserInputService")--The UserInputService service

UserInputService.InputBegan:Connect(function(input)--Fired when an input begins
    if input.KeyCode == Enum.KeyCode.LeftShift then--Checks if the KeyCode equals to LeftShift
        Camera.FieldOfView = 80--Sets the cameras field of view
        player.Character.Humanoid.WalkSpeed = SprintSpeed--Sets the walk speed to SprintSpeed
        player.Character.Animate.walk.WalkAnim.AnimationId = ("rbxassetid://6708766874")--Sets the walk animation to your walk animation
    end 
end)

UserInputService.InputEnded:Connect(function(input)--Fired when the input ended
    if input.KeyCode == Enum.KeyCode.LeftShift then--Checks if the KeyCode equals to LeftShift
        Camera.FieldOfView = 70--Sets the cameras field of view
        player.Character.Humanoid.WalkSpeed = NormalSpeed--Sets the walk speed to NormalSpeed
        player.Character.Animate.walk.WalkAnim.AnimationId = ("rbxassetid://6706074754")--Sets the walk animation to your sprint animation
    end
end)
--//Go to both of animations and set the to animation priority to "Movement" and toggle looping for both of the animations that should fix everything\\--

You need to use UserInputService and get the input because it updates everytime when you unpress your key so it unfunctions. Getting the KeyPress using player:GetMouse() is not recommended for now.