Can someone explain to me the role of these two capacitors C1 et C2 in the external quartz circuit

 

Off the top of my head, one simple explanation is - crystals are tuned circuits. Loading capacitors help to lock in to the resonant frequency.

Another reason is - crystals have different modes of oscillations, most commonly, fundamental and third harmonic.
Capacitors help the crystal to oscillate at one preferred frequency.

You can read this:
http://www.ti.com/lit/an/swra372c/swra372c.pdf

 

Thank you

 

Here's a more lengthy discussion: http://www.ti.com/lit/an/slaa322b/slaa322b.pdf No longer available.

Crystals will usually come with a load capacitance specified. There is sometimes doubt about what that means. Here's a simple description: https://community.nxp.com/thread/388856

 

The capacitors are there to resonate with the crystal inductance and cause the crystal to oscillate on its fundamental parallel-resonant mode. ... The difference between a crystal with two capacitors compared to a ceramic resonator is that the capacitors happen to be integrated into the ceramic resonator.