Legal Question in Criminal Law in California

If it is truly an automatic weapon, then it is illegal.

I am assuming that your term "floating barrel" means the rifle's barrel was isolated from everything forward of the chamber of the barrel. In that situation, the only parts of the barreled action (which consists of the receiver and barrel as a unit) that touch the stock are the receiver and the fatter chamber portion of the barrel - everything forward of the chamber touches nothing. This is done to prevent inaccuracy caused by the barrel heating during firing and expanding against the stock.

Floating the barrel alone, in such a case, would not make a rifle illegal, unless the barrel were also shortened, so that its length was less than 16 inches, or the overall lenght of the rifle was less than 26 inches. (Pen. Code, sects. 12001.5, 12020 subds. (a), (c)(2).)

I would be very careful about calling a gun an automatic weapon, just because it looked like one. The definition of an automatic weapon is defined by how many times it fires in relation to a pull of the trigger, and not by how it looks.