I'll really like to know if Electrum or Bitcoin Core is free.
What do you mean free? Do you mean transaction fee? If I were you dont be a fan to those wallet service that has no transaction fee all of them are suspicious.
No, I mean getting the desktop software
If that's what you mean then all of them(all wallet service/software) is free to download just to make sure that you download it from the official website of the particular wallet you want to use and make sure that your computer is safe from malicious malwares.