As I have heard and seen the word risible used, it has always meant something like ridiculous or preposterous, even spurious.
However, this is a somewhat accretionary meaning that has developed over time since the word came over from French. It is originally descended from the Latin word ridere, which means to laugh, combined with the suffix -ibilis, meaning to be able. So, risible means something that is able to be laughed at.
This meaning holds in modern English usage, we also have the word laughable, which means the same thing Both laughable and risible bring with them an implication of dismissiveness, by which I mean that it is generally understood that if someone describes, for instance, an argument you are making as laughable, they don’t literally mean that they found it funny or actually laughed when hearing it. Rather, rather they mean that it was of such poor quality that it was deserving of ridicule. The concept of laughter is being used in this instance as an intensifier to communicate an insult and, in this respect, both words are the same.
However, there is something about risible that has always seemed more intense to me, something that makes its use more insulting than calling something merely laughable, and I belive it stems from the non-English origin of the word. The meaning of most compound words based at least partially on a native English word (in this case, laugh) is usually understood easily because one understands the words on which it is based.
This is not always the case with borrowed words, a problem which is particularly acute in English due to the heavy French overlay that came with the Norman conquest. Even if one knows the definition of a word, there are times when loan words happen to correspond with words in the receiving language and the meanings become unintentionally intertwined.
I feel that something like has happened in the case of risible in that it bears an unmistakable, though purely arbitrary resemblance to the word ‘rise’. This is a subtle connection that is likely to be made only subconsciously, along the following lines: while something that is laughable might provoke scorn and derisive laughter, something that is risible is so outrageous that it provokes a reaction, specifically one in which the offended party rises to challenge the speaker.