McDonald’s Corp. has come up with a new value menu that it hopes will attract cost-conscious customers after years of losing traction with its existing low-price selection.

The new “McPick 2” menu, starting on Jan. 4, will allow customers to pick a pair of items for a total of $2 from among four choices: the McDouble and McChicken sandwiches, a small order of french fries, and mozzarella sticks.

Finding...