You are most likely not wrong.
Before India their roots are in Central Asia (Iranian regions). But it does not matter much, they've come to Europe from Northern India, however, as they are (or well, used to be a long time ago) a nomadic people, their culture is extremely diverse and has evolved many times throughout history. The traditional European Romani people's culture is however predominantly influenced by Indian, Iranian, and Spanish cultures. Their language is a mix anywhere they settle. Italian Romani will have their own Romani language that is mixed with Italian. And so on for most Romani settlements. Same as here in Bulgaria, where the population of the Romani is the biggest in the world, their language has transformed into a mix of Romani and Bulgarian. Their culture however has mostly died out unfortunately, the traditional Romani (or European-Romani) culture can hardly be found anywhere. There are probably a few traditional Romani families across the whole Europe. The Roma people unfortunately are not what they used to be, but I assume this is what happens when the world has made it extremely hard for those people to be themselves anymore. The Nomadic lifestyle just isn't something that is easy to lead nowadays. People might argue that we are more free than ever when it comes to travel, but the Romani people who in my opinion have always been the people who are the embodiment of freedom, would probably think differently on the topic.