Turntable Causes Speaker Cones To Excessively Move Rapidly

Did you remove the cover and put the turntable on some kind isolating platform?

Your speakers have a rear port, close to your TT. They should have included port plugs.

I would 1st move the speakers a bit further apart, and toe them in facing the listening position which ’aims’ the port away from the TT somewhat.

Next, I would plug the rear ports.

AI Quickie:

"Yes, the Focal Sopra No. 1 features a rear ported design with a slot port. 

• The cabinet includes a small rectangular port at the rear to load the bass unit. 

• The speakers come with foam port plugs that allow users to seal the ports if desired, which can help with subwoofer integration or placement in enclosed spaces. 

• The port tuning frequency is approximately 55Hz, providing solid bass response down to about 50Hz." 

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+1 on port plugging.  Driver excursion below port tuning frequency rises very rapidly, so even moderate rumble can be very problematic.

Also, honestly, a good experiment for everyone.  Port plugging is a good way to tune speakers for a room, even more when a subwoofer is being used.  Plug the port and raise the sub Hz is usually quite complementary. 

I had your exact problem with my Technics SL-1000R turntable and a Hana Unami Red MC cartridge. I also have REL Subs x 2 allthough my system is on a suspended floor. I spent every evening and weekend for a couple of weeks trying to find a solution - I ultimately gave up and bought a Burmiester 174 Turntable that fixed the problem. I can offer some tips for things that did make some progress for me. 

1. Added 7x subfloor jacks in my crawlspace (doesnt apply to your situation) 

2. Made adjustments to how the washers that hold the platter were installed and how tight the screws holding the platter were tightened. (this made a pretty big difference) 

3. Added IsoAcoutics Iso Pucks below the Subs (this was probably the biggest improvement) but it still didn't completly fix the issue

4. Added IsoAcoutics isolation platform (Didn't help much) 

5. Used a MOFI Heavyweight Record Weight (Didn't help much) 

6. Hired a "pro" from the audiophile store to come over to my house to make finite adjustments to everything (waste of money) 

7. Hired another "pro" to come over and make more assessments (didn't help much) 

Finally gave up and bought a different turntable and That Finally Fixed It! 100%

Through it all, the washers in the platter made a big difference and the Iso Pucks under the Subs were the biggest improvement but ultimately I couldn't get it figured out completely 

I did all of the modifications myself after speaking with loads of knowledgeable people. I added the Isoacoustic footers (which did little). I then installed the upgraded tonearm (which did little to help). I then added an isolation table (again didn't help). Changed phono cartridges (A Kiseki to a My Sonic Labs which didn't help). Changed dual subs (From Rel 212SX to Rel #31's which didn't help). It was only when I ordered a new main bearing for the platter and did that installation myself that I realized the motor was actually not tightened down properly. That was the problem all along. A long and expensive journey but now worth it to me in the end because I really enjoy my vinyl music. My belief is that you have something loose within your turntable creating the vibration which carries through your system to the speakers. I hope this can help you.