During the 20th century, we have already seen the loss of hundreds of languages in favor of more international and widely-used languages. The United Nations, for example, uses Arabic, French, English, Chinese, Russian, and Spanish as its official languages. Within the near future, i.e. the 21st century, to what extent will this continue? Approximately how many languages will still be spoken fluently (ILR>3) by a significant portion (>0.1%) of the world population past 2100, and which languages might they be? (Note: This is not a duplicate of this question; that question refers to 2500, while this question asks about the relatively near future.)
I think you'll find that this question is far more complex than you had ever imagined, and that is because humans are complex creatures. With ~7 billion people making choices based on their own individual needs and desires, making accurate predictions becomes about as easy as predicting next year's weather for a specific locale.
Take a look at the Hawaiian language. Sixty years ago, it was headed towards extinction. Its use in public places such as schools had actually been banned. But a wave of cultural interest brought it back to life, and now there are immersion schools in which students speak nothing but Hawaiian. I doubt anyone would have predicted such a thing in 1960. Something similar happened with Irish Gaelic.
At present, India would seem to be a likely place for language consolidation. There are dozens (if not hundreds) of local languages spoken in India. As a whole, India could probably benefit from settling on 1 or 2 languages for everyone to speak. But languages are deeply personal, and something that people don't give up easily. History shows that they have a way of sticking around even in the face of political pressure.
For the near future (within the next 100 years), I doubt there will be much change from the status quo. Spanish may gain influence if the Latin American countries ever emerge as world powers (either collectively, or one or two on their own). People in the world of business may begin learning Chinese in greater numbers, as a second language. But Finns, Greeks, Nepalese, etc. are unlikely to stop speaking their respective languages in favor of one of the big 5 or 6.
To quote from the wikipedia article on endangered languages:
Language shift most commonly occurs when speakers switch to a language associated with social or economic power or spoken more widely, the ultimate result being language death. The general consensus is that there are between 6000 and 7000 languages currently spoken, and that between 50 and 90% of them will have become extinct by 2100. The 20 most common languages, spoken by more than 50 million speakers each, are spoken by 50% of the world's population, but most languages are spoken by fewer than 10,000 people.
Language extinction is a complex issue. Assessing the health of an individual language is based more on the average age of the speakers than the total number of speakers. Since the biggest factor for a language's survival is young people speaking it, a lot depends on educating the next generation of speakers. There have been some very successful efforts to revitalize dying languages in places where preserving cultural heritage is important. Simultaneously discouraging the speaking of native languages is a common tool of governments looking to control ethnic minorities.
Since life expectancy keeps increasing there will not be any major changes to what languages are spoken in the next century. After all today people will be born that will be alive in 2117. Thus there are not enough generations to change anything regarding the linguistic level that comes to nation level languages we have today. French people will keep speaking french in the 21st century.
Languages that are in danger to disappear are languages talked by small minorities, like Eskimo tribes that only have a mere few thousand members. Such languages, that are spoken by merely a few thousand or less people, will likely disappear, as such people don't teach their old language to their kids. The process is sped up as these people move to cities where nobody will speak their rare language. Thus, no matter what you do, such minor languages will erode as the chance to use it anywhere is none.
However, english likely becomes even more of a global language that most people can speak, regardless of their nationality.