Fog and Edge Computing infrastructures have been proposed to address the latency issue of the current Cloud Computing platforms. While a couple of works illustrated the advantages of these infrastructures in particular for the Internet of Things (IoT) applications, elementary Cloud services that can take advantage of the geo-distribution of resources have not been proposed yet. In this paper, we propose a first-class object store service for Fog/Edge facilities. Our proposal is built with Scale-out Network Attached Storage systems (NAS) and IPFS, a BitTorrent-based object store spread throughout the Fog/Edge infrastructure. Without impacting the IPFS advantages particularly in terms of data mobility, the use of a Scale-out NAS on each site reduces the inter-site exchanges that are costly but mandatory for the metadata management in the original IPFS implementation. Several experiments conducted on Grid'5000 testbed are analyzed and confirmed, first, the benefit of using an object store service spread at the Edge and second, the importance of mitigating inter-site accesses. The paper concludes by giving a few directions to improve the performance and fault tolerance criteria of our Fog/Edge Object Store Service.