The plot would be much more complex. Harry could easily defeat Voldemort with the combined power of the Infinity Stones. So the main conflict of the original story would be resolved very quickly.
If Harry had the Infinity Stones in fanfiction, the plot would change drastically. Instead of relying on his friends and Hogwarts for protection and power, he would have the Stones' abilities. This would likely lead to a more solitary journey as he might think he doesn't need anyone else. Also, new villains might emerge who are after the Stones, creating a whole new set of challenges that are different from the fight against Voldemort.
The plot would be transformed in numerous ways. For one, the political landscape of the wizarding world would be different. With the Infinity Stones, Harry could enforce his own ideas of justice and order. He could use the Power Stone to enhance the defenses of Hogwarts to an unbreakable level. The Time Stone could allow him to explore different timelines and gain knowledge that was previously unavailable. This new knowledge might lead him to make decisions that would change the relationships he has with his friends and mentors. And his relationship with Dumbledore, for example, might become more complex as Harry's power grows. Also, the story would no longer be just about the fight against Voldemort, but about how Harry manages the power of the Infinity Stones and the new threats that come with it.