Until January 2008, ICAO's standards and recommended procedures (SARPs) required only that aviation personnel in contact with international flight operations master a set of words and phrases known as "ICAO Radio Telephony Phraseology." As you might imagine, there is a significant difference between a relatively limited set of technical aviation terms and true language fluency and proficiency, especially in a language as large, nuanced, and complex as English.
The International Civil Aviation Organization has decreed that from January 1, 2008, all Air Traffic Controllers and Flight Crewmembers engaged in or in contact with international flights must be proficient in the English language as a general spoken medium and not simply have a proficiency in standard ICAO Radio Telephony Phraseology.
Although English is the preferred international language of aviation, pilots and controllers within a non-English speaking country's airspace may use that foreign country's language.
ICAO allows a pilot and controller to communicate in any language with which they are both familiar. In France, French is commonly spoken between French pilots/controllers; in Spain – Spanish; in Russia – Russian. This is true to the extent that much of the world finds it to their advantage to speak English.
During an international flight, it is not unusual to be on a frequency where multiple languages are being spoken. This practice can diminish the overall situational awareness with other air traffic maintaining a "listening watch." Even with a careful listening watch, only part of the situational awareness flight picture can be achieved. This practice can put the English-speaking US pilot at a distinct disadvantage in the international flight regime.
International standards of phraseology are depicted in the International Civil Aviation Organization (ICAO) Annex 10 Volume II Chapter 5 and in ICAO Doc 9432 - Manual of Radiotelephony. Many national authorities also publish radiotelephony manuals that expound upon ICAO provisions, and in some cases modify them to suit local conditions.
Advanced Aircrew Academy has an eLearning module that can be included in your International Procedures training on ICAO Phraseology.