Hey you should be able to find movers under Guides>Professional services>Movers....talk to some one that has used these services should be reasonable.....

Go to IKEA in Geneva to decide what you want, and then order it from IKEA France, they will deliver it to your door. https://www.ikea.com/ms/fr_FR/customer_service/transportliv.html

We live in Evian, but buy some of our household goods on a website [which is free btw], called Leboncoin. It is free to register and then if you speak French, you can peruse what is availabe - heaps of furniture, lots from Ikea, under the section "ameublement". You simply have to put in the postcode 74500 and it will display what is on offer.

Shopping in Switzerland and importing furniture into France might be costly, albeit that there are very rarely any customs controls at the border outside Douvaine. You wouldn't want to pay duty on new items, that's for sure!

Order online from IKEA france, as Tawb suggested, or go to any of the several furniture stores in Ville la Grande/Annemasse along the route de Thonon D-1206 (which is the road from Evian to Geneva).

If you want Ikea-quality low price furniture, there is a BUT store in that area (https://www.but.fr/magasins/127/But-Annemasse.html) and they will deliver (https://www.but.fr/Services/Page/Livraison-domicile)