All inch sights fold down. Australian, Canadian, British, etc. They fold out of the way for the Trilux SUIT scope. It can also be used to fold out of the way of a conventional scope as a side benifit. They are primary sights, they just also fold out of the way.
Most FAL sights wiggle around some. The Metric sights are usually the worst once they get worn. The rear sight on your rifle is held in place by a detent/spring arrangment that actually keeps the rear stight from movign around too much. It also allows you to make range adjustments by just sliding the rear sight up and down the range markings. If your rear sight is moving around a bunch, then it could simply be worn out (the rails are worn), or the spring could be weak. Inch sights in good condition don't wiggle.
Inch sights are also "high" in profile. Metric sights come in "high" (like the Israeli, or very early FALs) or "low" (like the G1, or SAR-48). A compatible height front sight block needs to be on the rifle, so make sure you stick to either inch or a "high" metric rear sight.
A good path to take is to put a scope on it and just use the sights you have now as back-up flip sights.
Ross