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The Kingdom of Saudi Arabia does not currently issue tourist visas for residents of any countries, including France. They have announced that they intend to change this policy next year (2018). However at this stage no further details on that have been released.
The press release you have referred to almost certainly applies to those obtaining business visas, which are available to verified business travelers. However these are generally very expensive and require a significant amount of paperwork to obtain.
Specifically for visiting the Jeddah area there is also a Hajj visa available. However the rules around these are strict - they are only issued to bona fide hajj pilgrims, and you are not allowed to stay in the country beyond the end of your Hajj Pilgrimage. So even if you are a Muslim, it will most likely not be suitable for what you are after.