I have a PD100 XLR adapter that I use with my Sony VX-2000 to give me a single phantom powered XLR input which I use with a boom and shotgun mic on interviews. I got mine off of eBay for about $50 but you can buy them new from Sony for $204.42 here:

https://servicesplus.us.sony.biz/PartsPlus.aspx

Do a search for a A7094044A

Will this hotshoe to XLR adapter work with the FX-1?