Yes, this is really confusing. It always seems to be defined elsewhere as "to wish". I guess it makes sense as a loose translation, but "loose" translations are usually WRONG in Duo. Has anyone tried "would wish"?
Indeed, "They hoped to sign this contract quickly" gives slightly different hue to it; something that maybe didn't happen even if they had such a wish: in French it would correspond to "Ils espéraient signer ce contrat rapidement"