A company I'm looking at claims to have made the website for an airline and a furniture store using Django, but when I look at the sites, there is no indication what the underlying web technology is. How can you tell?
Try to navigate to some 404 error page, or something of that sort. Chances are slim, but try to find a default django error page.
You can also try to login to www.website.com/admin
and see if you get the default django admin page.
Other than that, if that didn't work, then you just can't.
You can try a few things, such as attempting to find error pages, and checking the default location of the administration panel that Django creates, but overall there's no way to determine what technologies a given site is using.
There are no reliable indicators to my knowledge but you could check the /admin/ URL to see if you get the standard admin app or sometimes the feed-URLs use a common prefix compared to a common suffix (although this might not be an indicator at all but just a preference of the developers).
Trying to trigger a debug page (either via a 404 or using some broken input that might case an internal error) might also be a good way (although this acts more as a test of competency of the original developers and admin than anything else :-) )
Could you ask the airline and / or the furniture store? I'm guessing that you want to know if this company has good experience in django, I think it is reasonable to ask for references if you are considering working with them.
The other companies may be quite happy to discuss what technologies were used - some are and some aren't, but it's worth asking.
Navigate to a page with a formset, and check if there are *-TOTAL_FORMS or *-DELETE hidden inputs. That doesn't prove that they are using Django, but might be a clue that they are (with the mentioned model formsets).