I think that the lawyers could argue for ages over this question.
If your whole journey, from Dubai to Edinburgh, was booked with Air France and
if they indicated that your flight plans allowed enough time for the connection, you
might be able to claim back the full cost of your flight from Dubai to Edinburgh
if your delay was
over 5 hours (even by a minute or two).
The EU regulation apply to all flights operated by airlines licensed by an EU member state, irrespective of the point of departure. So there's no doubt that the rules apply for a departure from Dubai. For delays of less than 5 hours, you have no right to any financial compensation; you're only entitled to receive appropriate meals and refreshments. Once the 5 hour threshold has been reached, you're entitled to a refund of your ticket price:
http://www.rcn-ifna.org.uk/html/eu_delay_compe nsation.html
If your flight from Paris to Edinburgh was booked separately from your flight out of Dubai, you might find it much harder to get compensation. Air France could say that they completed their contract, without excessive delay, to get you from Dubai to Paris. If you then tried to claim compensation for missing your next flight, Air France might claim that you'd allowed insufficient time for the connection. (Most airlines specify a minimum connecting time of 2 hours at major airports. Some specify 3 hours).
Chris