How can I apply for a Non-O visa based on marriage while in Thailand?

Okay, enough of the "we talked to an agent" b/s (as the group has a ZERO tolerance policy about discussing things like that).

You can get a 90 day Non-O visa issued inside the country based on being married to a foreigner who legally works here. Depending on the immigration office you use you would need between 15 and 21 days left on your current entry stamp (30 day visa exempt, 60 day tourist visa or a 30 day extension from one of those). You apply it goes under consideration for 14 - 20 days and then you go back and get the 90 day Non-O visa inked in.

You should go to the immigration office in your area and get the hand out that lists the required documents. That visa costs 2000 baht.

You are confusing a bit. Non-O visa based on marriage to a foreigner working legally is same one to so-called dependent visa in this case. But yes, you need get Non-O dependent to a foreigner with valid Non-B or extension and enter Thailand on it, then apply extension as dependent (spouse) to a foreigner who is on extension based on working.

And as you are French passport holder, you can apply Non-O being dependent to a foreigner working legally at many consulates in South East Asia.

You can only get a Non Immigrant O visa based on being a dependent of a foreigner working in Thailand. You get this visa at a Thai consulate.