It is only to be found in the Pyrenees at the moment. A population is being established in the Italian Alps so conceivably that could expand and eventually reach France.
The problem for Brown bears would seem to be that they not only threaten the sheep and cow populations but also man. Whereas the Lynx will definitely avoid man and despite popular stories the Wolf is most unlikely to attack man. Most attacks in the past were from Wolves that had become rabid. However there is really no reason why Bears should not populate areas where man is also populous as for example in New York state there are approximately 5,000 bears.
The place I saw a bear was in Siberia at Lake Baikal and below are a series of photos from that trip. We nearly saw them on our way to the fishing village on the edge of the lake called Barguzin, we heard them growling and we saw plenty of footprints. We had got stuck in the snow. However eventually we did get to the village, not the most well-appointed village as you can see.Tthe next day we set of on a snow sledge with a driver (he is the one with the fur hat, which he told us was made by himself from his friends dog after it had died) and ranger across the ice to an island in the lake where the warden thought we might see Brown Bears. We did and it was initially at the edge of the lake where the ice was melting and there was some water. From this water Mayflies were hatching out and the bear was feeding on them. I was surprised that such a large animal would feed on something so small, but I suppose Whales feed on Krill so why not.
The bear did not stay beside the water long and headed back into the woods. I only had a small Olympus digital camera in those days so the quality of the shots is not so good but he is clear to see. We then moved on and out across the lake, the warden( the guy with the gun) had a good look round to see if he could spot some Baikal Seals which we did and got reasonably close before it disappeared down its hole. Incidentally the warden did explain that he had never shot a bear the gun was there to warn it off if it got too inquisitive and in the very unlikely possibility that it took no notice then ultimately he would shoot it.
Although the photo quality is limited you can click on the photos to see them in more detail.