A Persian victory at Marathon leads to a Persian takeover of Greece in 490 BCE. This leads to Persians overrunning Athens in 485 BCE.
Persian Invasion of Greece
By 470 BCE, all of Greece except for Sparta was taken over by Persia. The Persians began to attempt to siege the Spartans into submission. Large numbers of Greeks began to flee to Sparta, heavily overpopulating the city-state. More and more food needed to be farmed. This led to Sparta becoming more and more unstable. Several rebellions in the 450s BCE began to destroy Sparta. A civil war began to break out while 25% of the population of Sparta died of starvation. The ruler of Sparta was killed by his own guards and these peoples surrendered to Persia in 430 BCE.
Flight of the Greeks
Many Greeks fled to Italy, where Greek colonies were already established. This almost complete swamping of Italy eventually led to the region becoming known as New Greece, or Nova Graecia by the Romans. However, the New Greeks slowly invaded and conquered Etruria, Rome, and the rest of Italy. This was complete by 405 BCE.
In southern Keltia (OTL France), Greek settlers fled there as well. They came in direct conflict with the native Keltoi. The more populous and civilized Greeks prevailed and a treaty was signed in 403 BCE, expanding Greek control to all of Keltia.