Another word for "Compete with" in the context of Languages
How about vie?
vie, verb (used without object), vied, vying.
- to strive in competition or rivalry with another; contend for superiority
A phrase that is often used in situations like this is vie for dominance (Ngram). You could say:
Scientists predict that Language X will vie for dominance with English in terms of global usage.
How about rival?
Having the same pretensions or claims: competing
Merriam-Webster Dictionary
Transitive verb
1 : to be in competition with