Well, literally, it translates to «J'aimerais devenir capable de parler français». However, it sounds a bit strange in French because «devenir capable» (i.e. become able) isn't a phrase people commonly use. I might say instead simply, «J'aimerais être capable de parler français». But personally, I would probably use the sentence «J'aimerais pouvoir parler français» which expresses the same idea, but instead of saying 'I am able', it says 'I can', which is a more direct form, so tends to feel more natural when you say it.

As a French learner, I've summarized several ways to express "I'm able to" . 1. Je peux 2. Je suis capable 3. Je suis en measure de ..