Currently, Ragnarr Loðbrók exists as a legendary figure, but at this point there is not any definite proof that he actually existed. There are quite a few accounts of people with variations on the name Ragnarr, who match the time and accounted places that Ragnarr is said to have visited.

The Frankish Chronicles place a Reginheri sacking Paris in 845. However, in the accounts of this, he and most of his men are reported as dying either during or not long after sacking the city. This is thought to have been for the purposes of Frankish propaganda, but there is nothing to completely prove this. Also in France, there is a Raginarius who was given land in 840 by Charles the Bald. Outside of the Frankish lands, Ragnarr Loðbrók is also described as raiding in Ireland by Saxo Grammaticus and the Krákumál. Irish chronicles place a Reginheri and a Norse king named Ragnall, who raided Ireland after 851. There is a possibility that Reginheri and Ragnall could be the same people, but ultimately there is nothing definite linking the two. Unlike his sons' invasion, Ragnar's raids in England are not even mentioned in the Anglo-Saxon Chronicle.

In addition to his travels, the name Loðbrók is only mentioned with the name Ragnarr in Norse sources dating at the earliest to the 11th century. Other sources only use Loðbrók when discussing his sons and even then they mention different lists of sons and/or various spellings of Loðbrók. Rory McTurk suggest Loðbrók may have been a female name rather than that of a male. As evidence for this, McTurk cites a runic inscription from a tomb at Maes Howe, Orkney, which refers to Loðbrók as a female.

Ultimately, unlike some of his sons, we don't have conclusive evidence that Ragnarr Loðbrók was anything more than a legendary figure. Ragnarr is noted by different sources as separately dying in France, Ireland, and England. There is also a lack of connection between these various Ragnarrs and the name Loðbrók.

Sources:

Studies in Ragnars saga Loðbrókar and its Major Scandinavian Analogues by Rory McTurk

"Introduction" from The Sagas of Ragnar Lodbrok translated by Ben Waggoner

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