If you're open to phrases, the closest I could think of was respectful language or respectful discourse. This is often used in schools to tell kids not to curse. However, it encompasses more than just a lack of curse words. It also includes not using language that is disrespectful, hateful, offensive, etc based on race, religion, sexual orientation, or other groups targeted by prejudice and discrimination.
Two possible alternatives are clean language* and polite language. Clean is used when the curse words have been censored in a song, often "clean version".
One of the dictionary entries is
- inoffensive in language or content; without obscenity. (Dictionary.com)
Polite again would include more than just lack of curse words. It would include other well-manner, refined language.
Three more less formal alternatives are PG language, G-rated language or family-friendly language (as @Willow suggests).
PG and G-rated come from the MPAA film ratings.
- PG Rating
A PG movie rating stands for Parental Guidance, as some material may not be suitable for children. There may be mild strong language and some violence, but there will not be substance use or abuse.
1 : having a rating of G; broadly : relating to or characterized by a lack of violence, obscenity, or sexual explicitness • a G-rated novel
2 : innocent, clean • G-rated fun
In common usage, PG is used to say no curse words, especially strong curses, like the F and S words. It could also suggest language without other obscene materials. Example: Hey, keep it PG!
As it suggests, family-friendly language suggests that it is suitable for families. It would imply no curse words, but again, it could also suggest language without other obscene materials.
* A cursory Google search shows that this has some kind of special meaning in psychology, but the context should clarify that you're talking about language without profanity.