I think almost everyone attempting to acquire a new language confronts this basic challenge.
My personal feeling is that the core processes of the brain (of most people) are fundamentally social in nature and that language is the sine qua non on sociability. Therefore, this experience of things "in the back of your mind" makes perfect sense. Your ability to trust what is in the back of your mind will almost by necessity have to grow out of experience in real-world exchanges with other people.
It's only by exchanging the tokens of language that you can really start to depend upon and trust the stuff that is going on in the back of your mind. That's the point at which language begins to be "solid" -- for everybody. And I think it is basically the same process when picking up a new lingo in your primary language.
I think it is also clear that people have varying degrees of natural ability to imagine social situations and trust them and learn from them in the sense of inhabiting (in a deep way) a virtual reality that can trigger the same physical processes in the brain that real-world social situations create.
I believe the concept of "language emersion" is something that you should attempt to strive for even when you are all by yourself. This can spawn advice that discourages you from translating too much. And that is good advice, but like everything else, you can take it too far. Each person has a unique brain that will learn better in some situations and worse in others. Each person has certain thresholds of comfort in how much the can trust their instincts, let go, and "use the Force" (to go Star Wars on you).
If you have an overly critical brian that just can't let go of consciousness, then you might try to enforce "closing the loop" back in to French every time you "pop out" and start thinking in English. In other words, if you find yourself translating French into English, then figure out how to cycle back into French in a manner that trains your brain that there isn't anything to gain by jumping back into English because you already "know" it in French.
Get back completely into French by thinking about translating the English instead of the French. Imagine that the English is the unfamiliar or strange form and not the French. Just attempt to acquire that feeling or attitude. Trust and believe in the consequences of utterances in French, and less so on grammar and technical things -- try hard just to "wear it." Also, to the greatest extent possible, move your "thinking about French" and the explanations for why something makes sense fully back into French.
When you find your brain is constantly being triggered for some kind of explanation of something. Try to get to where you can explain it in your French mind. There's a Russian saying that I can never get far from. It is: "Repetition is the mother of all learning." As Olivier is saying, there's just no substitute for it. But there are usually ways to "enhance" the effectiveness of repetitions. So, I say choice number one is increase social interaction around the language you are trying to acquire in the real world. Choice number two is to be more diligent about creating virtual experiences in your mind. Be a kid. Say silly things. Tell simple, ridiculous stories to yourself. And use the Force. And of course choice one and two are hardly mutually exclusive.
These are just some thoughts about the question. It's not clear to me that they are the best ones or the right answers for anybody in particular. And it's certainly not any kind of "recipe" that claims any specific results. =)