Any manner of wet cleaning should be safe, although it doesn't look very soiled so probably doesn't need much. The source of the rug might be India, but it isn't a dhurrie and it looks to be a fairly new and trendy pattern.
Given the condition of the fringe it's already been bleach washed at the point of manufacture so dye bleeding won't be an issue, but fringe falling off might be. I'd tug on that fringe and see if it comes off easily. If so, the customer needs to know a lot of it might dissolve just with rinsing.