You can get some information from the French Embasy web site at https://sa.ambafrance.org/Applying-for-a-French-visa-in-Saudi-Arabia.
You'll need to complete an application at https://france-visas.gouv.fr. The fee is 118 Saudi Riyal, if I've understood the site correctly.
You may need to attend an interview at one of the French consulates in Jeddah or Riyadh.
I couldn't find an estimate for the processing time on either site. You may have more luck. All the processing services offer a tracking tool so that you can follow the process.
France is in the Schengen area. Schengen visa validity is often based on the duration of the trip you put in your application form. Expect to get a visa that's valid from a few days before you intend to arrive, to a few days after. This gives you some flexibility to adjust your dates if you need to. The duration of stay might match your intentions closely, so you can stay, say, a total of fourteen days in a period of one month, for example. This isn't always the case, so check the validity and duration of stay carefully when you're booking flights and hotels.