Correct. However if you fly in on DL, then DL is usually willing to rebook you if you misconnect. No hotels, and no getting put on OAL except possibly for JV partners AF/KLM. Even then they'll usually want to make you stay on DL. However since they pay half your fare to AF/KLM regardless of if you fly DL some will put you on them. If it looks like you'll misconnect you can even ask in SJC about rerouting the CDG ticket to start elsewhere and getting you there.

Again no obligation, but DL is good in this regard. Note ask at the airport. A reservations agent won't have the power/clout to get what you need done.