This would work, though "the current language" or "the present language" just wouldn't be said. However, "the present-day language" would be a valid alternative. Both are natural and readily understandable ways to refer to Spanish (in this case) as it is used today.

It certainly has to be "THE contemporary language", not just "contemporary language", because without the article it would mean "lenguaje": the kind of language people use.

"Contemporary English Pronunciation: A practical workshop
[...] The course will also
• include new developments in English, with discussion of both phonetic and social-cultural factors which have shaped the contemporary language."
https://www.ucl.ac.uk/psychlangsci/students/professional/543...

"We have conspicuously omitted variation in time, since this book is solely concerned with the grammar of present-day English. Variation in the contemporary language, however, reflects in part historical changd in progress."
Quirk et al., A Comprehensive Grammar of the English Language, p. 16
http://es.slideshare.net/ivana14jovanovic/a-comprehensive-gr...

In this second example, the leading experts on English grammar use "the contemporary language" to mean "present-day English".

"Wherever possible comparisons are drawn between Old English and the present-day language"
Richard Hogg, An Introduction to Old English
http://books.google.es/books?id=hR9wAAAAQBAJ&q="present-day ...