Welcome back to the Wefugees Community and thank you for reaching out to us.
With the subsidiary protection status, you are allowed and even obliged to (with rare exceptions) apply for a national passport at your country of origin's embassy. For recognized refugees, however, a visit/requested service at the embassy jeopardizes their refugee status and the residence permit in Germany.
I don't know if the embassy responsible for you is issuing temporary passports. I know that there is such a service available from German authorities, but I am afraid it is way more complicated at embassies.
And yes, your son needs a passport to travel to France - we discussed a very similar question here before. The good news is, however, that you don't need a visa to travel within the EU for up to 90 days.
I hope this helps and all the best,