There's a separate entrance for those with disabilities. You go next door/southeast side, through the gates (I think), but you cross the courtyard and you will be escorted to the Sainte-Chappelle entrance where there is a ramp and elevator. The sign is large and clearly indicated with the universal handicap (wheelchair) logo. You don't have to be in a wheelchair, just have a physical disability....at least, that's my understanding.
Now, the caveat -- I don't know if this has changed since the last time I was there. Given the heightened security issues, you may have to go through the metal detector (that long line).
It's worth trying, but I think it's for weekdays only, not the busy weekends. You may be able to use the tourist office to make a reservation.
Also, somewhere on some French version of info, I thought there is also perhaps a way to get a tourist disabilities card that will help in these situations, and perhaps give you reduced admission prices, or free, in some museums. Wish I could be of more help, but I never bookmarked any of this info.