Federal Civil Rights Liability
Qualified immunity is a doctrine that applies to lawsuits under 42 U.S.C. § 1983 seeking compensation for an intentional violation of constitutional rights under color of state law.
The qualified immunity inquiry is not reached in the first place if the prima facie case is not established because the conduct allegedly violating a constitutional right under color of state law, even if it is a well established constitutional right (i.e. one memorialized in a reported and controlling appellate court decision that is factually similar), if the action was merely negligent rather than intentional.
Thus, most likely, there is no federal civil remedy to the victim, unless even the use of the taser would have been a violation of a well established constitutional right under color of state law. Non-deadly force, like a taser, is subject to a lower threshold of justification than deadly force, like a firearm.
Of course, under general Fourth Amendment principles applicable to the states, an attempted arrest which appears to be what the OP describes, must be supported by probable cause that a crime was committed for which an arrest would be authorized. So, if this is the violation of rights alleged, there may be a federal civil rights remedy. But, further examination of the facts show that there was apparently a warrant for the arrest of the person shot outstanding. So the officer probably has a legal basis to use non-deadly force to make an arrest pursuant to the outstanding warrant, but probably did not have a legal basis to use deadly force to make an arrest.
Federal Criminal Liability
The most common charge under federal criminal law for excessive use of force by a police officer, is a criminal violation of civil rights. But this, like the civil remedy, requires a showing of an intentional violation of civil rights which the OP tends to suggest is absent unless the officer lacked probable cause to make an arrest.
State Law Civil Liability
At the state level, law enforcement officers acting under color of state law are immune from civil liability except as authorized by state law in an exception to sovereign immunity. Generally, there is no exception to sovereign immunity for a negligent use of force by a police officer.
So, the police officer probably can't be sued successfully by the victim's estate under state law.
State Criminal Law Considerations
For criminal law purposes, whether or not the law enforcement officer's actions were a crime under state law would dependent upon both the elements of the offense: probably manslaughter or negligent homicide in this case, and the scope of force authorized under state law in the case of a law enforcement officer seeking to arrest a fleeing suspect.
Usually, under state law, the use of reasonable force to make an arrest supported by probable cause is allowed and the use of deadly force to make an arrest support by probable cause is allowed only if there is a threat to the public based upon probable cause to believe that a particularly serious violent felony was committed.
Qualified immunity is not applicable to state criminal law liability, although express statutory defenses in a state criminal statute might be similar in some cases.
Of course, all of that analysis assumes that the story of the officer's motive and intentions was truthful. There is very good reason to be skeptical of this fact and to believe that the use of a firearm was not a negligent mistake, and that race was a motivating factor. Simply saying that one's motives were good is not a free pass and a jury doesn't have to believe the law enforcement officer.