Horizontal fire blocking when using rigid foam in basement?
You don't need to interrupt the foam insulation with fireblocking, but if there's a gap between the foam insulation and your framed wall, then you'll need fireblocking across the gap every 10 feet.

IBC 2015, 718.2:


  In combustible construction, fireblocking shall be installed to cut off concealed draft openings (both vertical and horizontal) and shall form an effective barrier between floors, between a top story and a roof or attic space. Fireblocking shall be installed in the locations specified in Sections 718.2.2 through 718.2.7.


While 718.2.2 designates a "concealed wall space" as requiring fireblocking, 718.2 (quoted above) prescribes the nature of this fireblocking: It interrupts "concealed draft openings." Building your framed wall tight to the foam will avoid any draft openings, but if you've got a gap between the framed wall and your foam, then that's a draft opening that will need a fireblock every 10 feet.