That's a fair point, but it sort of assumes that everyone in Britain today identifies with the English tradition of the mid C17th. I don't (my family isn't English) and neither do many others, so the English tradition is no more "mine" than the French one.
Also (and I may be wrong here), I thought the execution of Charles I was about an individual, who had been found guilty of treason, whereas that of Louis XVI was more about the monarchy as an institution (even though he too was tried as an individual).
Finally, I think the ideas of the French Revolution (for all their faults and all their negative consequences) were both more progressive and of wider longer term importance than the English Civil War and subsequent Commonwealth, so I'm happy to consider them as part of "my" tradition.