My understanding is that the Gauls didn't even have rights of citizenship until Claudius was emperor, which was about 100 years after the death of Julius Caesar. Is that correct?
When did Gauls and Celts have the ability to become senators?
Caesar did in fact make many Gauls and provincials citizens, and it really angered the senate and aristocracy. There was a joke at the time that Gauls would peel off their dirty cloths, put on a toga and ask "which way to the senate house?" In "Rubicon" it's argued that he does this in order to place high-ranking members of the provincial aristocracy in his debt to continue to support his establishment of an autocracy. Though other historians argue he might have done it as part of a long term plan for reorganizing the republic, since he was also granting citizenship to doctors and other highly skilled professionals who decided to move to Rome. He also might have been doing it to extend his populist reputation with newly integrated tax payers. Whatever the reason, the result was that the senate saw him as continuing to dilute their power and solidify his own claim to authority, which added fuel to the assassination fire.
This has been answered before in detail here.
But basically, no, it's not pure fiction, Caesar really did do that.
A followup question then: did any of these people or their descendents become major military or political figures in Rome?
Secondary question: were there people who opposed this? If so. Did this get added towards feelings leading up to assassination?