1. A Thai citizen can enter Thailand with an expired passport or even without a passport as long as he\she can prove being a citizen. However, one cannot go out of Thailand without a valid passport. As you mentioned your son is in Thailand based on his Thai nationality and not the French one - he'll need a valid Thai passport.
2. As a minor under 20, both parents must sign an approval at the passport office. As your wife is not present, she'll have to go to the Thai embassy in France or wherever she is and sign a POA for you to get there passport for your son.
I have recently done an official procedure for a minor Thai who's actually out of Thailand with both parents. At first they gave me a POA they've downloaded from a Thai embassy website, but the officials here demanded one issued at the embassy with all official stamps. Only after receiving the original POA I could complete the procedure.