Even if you have to stand in line for who knows how long and even if you have to eat your lunch from a paper bag while you stand in line you don’t want to miss the heartstopping smack in the face that is Sainte-Chapelle on a sunny day.
In more than one guidebook you will find the advice to try after 4pm for shorter lines which worked for us but I suspect the effect would be much less compelling without the sun, so if it’s sunny, get in line.