We spoke with Dr. Charles Sophy on "TMZ Live" Friday just minutes after the Princess of Wales revealed to the world she's dealing with cancer -- and he weighed in on how she and Prince William's children might be processing this heavy news about their mom.

Sophy -- a renowned child and family psychiatrist -- says lots of communication with the children, even about adult matters, is the best route to help them understand what's going on  ... and so is listening, as kids will ask the questions they want and need answers to.

Dr. Sophy says the Royal Couple needs to be transparent with their children -- 10-year-old George, 8-year-old Charlotte, and 5-year-old Louis -- and address the physical changes Kate may go through early on so the little ones aren't taken aback by things that may come.

On the issue of talking about really hard questions regarding the serious nature of the disease and how Kate's feeling throughout ... Sophy advises William and Kate to leave answers open-ended -- not promising a miraculous recovery, while also trying not to alarm the kids at the same time. He says it's a fine line ... one Will and Kate will have to walk together.

Since the young Royals are of different ages, some may question whether giving them varying levels of information is the right way to go ... but Sophy says no. He thinks William and Kate should give them all the same general information and let them process it how they need to.

Of course, Prince William will also be dealing with his own emotions following his wife's diagnosis ... and Sophy thinks it may bring up old emotions and trauma regarding the death of another famous Royal -- his mother, Princess Diana. Sophy says Will has to find the balance to weather his family through this storm.

Kate says she and her husband have already filled their children in on what's going on -- and that she's needed time out of the spotlight to do so correctly and with care.