I think "私は日本語を学んでいる" is better. 1.Word order is wrong Word order in Japanese sentences is different that in English. Because Subject is first, Object is second, and Verb is at the end. This contrasts with English's SVO word order. 2.present progressive form is wrong present progressive form of "学ぶ" is "学んでいる"

私は日本語をまなびます。(polite form) 私は日本語をまなぶ。(dictionary form) I will learn Japanese. Japanese sentences always end with the verb, which is totally different than English. You really can't do a direct translation, so you don't need いる in this sentence, , either 私は 日本語 を まなびます は marks the topic of the sentence を marks the object of the sentence As for me, I will learn Japanese