I would probably use the word diffident when someone is acquiescing to another's authority. The word connotes not just "simple" shyness, but also a lack of self-confidence and assertiveness.
Definition: (http://dictionary.reference.com/browse/diffident)
diffident
adjective
1. lacking confidence in one's own ability, worth, or fitness; timid; shy.
Another option would be timid. It's a fairly common word and I don't think I need to define it here.
To more directly put across the point of submission to authority, you can consider submissive.
Definition: (http://dictionary.reference.com/browse/submissive)
submissive
adjective
1. inclined or ready to submit or yield to the authority of another; unresistingly or humbly obedient:
submissive servants.
2. marked by or indicating submission or an instance of yielding to the authority of another: a submissive reply.
Obedient is another (more positive) option. Again, a word in common usage, and I won't be defining it here (it's easy to look up).
The most negative options, generally used critically, are pushover and doormat. They are idiomatic nouns that describe a person who seriously lacks self-assertiveness and may be defined as follows:
Doormat (http://dictionary.reference.com/browse/doormat):
doormat
- Slang One who submits meekly to domination or mistreatment by others.
Pushover (http://www.thefreedictionary.com/pushover)
push·o·ver
- One that is easily defeated or taken advantage of.
In the same vein as the above two, there is another idiom, which I believe is peculiar to the US: milquetoast.
Milquetoast (http://dictionary.reference.com/browse/milquetoast)
milquetoast
noun, (sometimes initial capital letter)
- a very timid, unassertive, spineless person, especially one who is easily dominated or intimidated:
a milquetoast who's afraid to ask for a raise.
And, as included in the definition of that word spineless is another negative adjective for someone lacking self-assertiveness. Again, it's a highly critical word. Given that the spine supports your body in an upright posture, I believe you should be able to see how the metaphorical meaning comes about.
Best Answer
I was going to say "it's all or nothing" (As @Rathony said in the comments). But then I did some websearching. Read on.
"do or die", like "life or death" and "life and death", implies you could lose a lot, but doesn't imply that if you don't lose, you win. Only that you survive.
"high stakes" implies that you could win a lot or lose a lot. But it doesn't rule out the possibility that you could also break even or just win or lose just a little bit.
If you want to say "win a lot or lose a lot with nothing in between AND it is much more likely that you will lose than win", then you could go with "hail mary pass".
"double or nothing" exists, as does the less common "double or quits", but I don't think they have the same idiomatic usage as you attribute to "quitte ou double".
http://dictionnaire.reverso.net/francais-anglais/quitte%20or%20double/forced does suggest "double or quits" - in the sense of getting out of debt, or deeper into debt.
The same site also suggests "make or break", which I think is the best answer yet, because it has more of a hint or randomness and unpredictability than "all or nothing" does.
So I'll suggest "make or break".