The article goes with language, so the following work as noun phrases:
the English language
The following doesn't usually work as a noun phrase referring to the English language. It would more likely be interpreted as referring to the English people:
Take a look at the following example sentences:
1a. I speak English.
1b. ？I speak the English language.
1c. ＊I speak the English.
2a. English is a beautiful thing.
2b. The English language is a beautiful thing.
2c. ＊The English is a beautiful thing.
Examples 1c is wrong. Example 2c is wrong in most situations. Example 1b sounds strange; we usually only say "the English language" when speaking about the language in the abstract or as a whole. Saying "English" always works, though it doesn't always sound as nice:
3a. By some estimates, there are over a million words in the English language.
3b. By some estimates, there are over a million words in English.
Both examples are acceptable, but example 3a sounds better.
Of course, there are other situations where you'd use an article with bare English, such as in the phrase the English of Shakespeare, but you can do that with any proper noun (see this answer). And if you're using English language as a modifier, it doesn't need an article because it's not functioning as a noun. In the following example, English language is inserted into the noun phrase a Q&A site as a modifier:
4. Stack Exchange is an English language Q&A site.
The article an belongs to site, not to English, language, or Q&A.
＊ means I think this utterance is unacceptable.
？ means I think this utterance is questionable, but not as bad as those marked with ＊.