Solidity, or Plutus, or IELE, or any other K-supported language, to write smart-contracts for the Cardano itself, and prolly JS/TypeScript to create a GUI that can be embedded into Daedalus and use its API to interact with it.
But it’s a speculation at this point, no official info on languages yet, afaik. The main point of the embedded app-platform, tho, is so that devs can create lots of applications without asking user to enter his private key in each of them. So any dApp can try to interact with existing user wallets thru API, but they would have to ask for permissions, and Daedalus would ask user for confirmation. Private keys would stay safe in the Daedalus itself.