What language do they use for international air traffic control?

English is the international language so I would assume that that’s what they’d speak.

English.

Although local languages are sometimes used in ATC communications, the default language of aviation worldwide is English. Controllers who do not speak this as a first language are generally expected to show a certain minimum level of competency with the language.

Latin.
That’s how scientists communicate, no?

Classical or ecclesiastical?

Pig.

English, or as this site puts it:

“Since clear and rapid communication is vital, commercial air pilots and air traffic controllers around the world are generally expected to speak English. Regional air traffic controllers may use their native language when they communicate with fellow citizens, but they also need to be able to talk with pilots from other countries. By dictating a universal language for aircraft control, all countries can be assured that air travel is smooth and safe for all.”

English, with the exception of “Mayday!”, which in French is “M’aidez!” or “Help me!” in the formal tense.

Yup, it’s English. I live in China and here it is also required that all pilots have a certain basic profeciency in English.