Philippe I was around 14 when the Battle of Hastings occurred and his mother's regency had only just ended, so what immediate reaction he had to William's conquest isn't recorded. On paper, William was still the vassal of Philippe as Duke of Normandy, which created the awkward situation of William being both a vassal and a sovereign in his own right. Since he'd replaced most of the nobility of England with Normans, that also meant that most of his nobles were, at least on paper, subjects of two different kings.

While we don't know Philippe's immediate reaction to William's conquest, we do have evidence of relations between them afterwards, which were variable. In 1077, they went to war with each other over William's attempt to conquer Bretagne. However, in 1079, they later become allies against the count of Flanders and William's rebellious eldest son, Robert Curthose. William and Philippe then fell out again 1087 over the Vexin, but that campaign ended when William was injured in battle and later died of his injuries. He attempted to split his realms by leaving Normandy to his eldest son, Robert, and England to his second son, William Rufus, but such a solution did not bring peace. Robert and William Rufus did not get along with each other, which meant that the Anglo-Norman nobles, who as I mentioned before, frequently held land in both England and Normandy, found themselves unable to be subjects of two men and endeavored to unite England and Normandy again under one ruler. In the end, William Rufus died in a hunting accident while Robert was away on the First Crusade. William Rufus had had no children, so their youngest brother, Henry Beauclerc, seized the English throne. Robert attempted to take England again after his return, but failed and ended up losing Normandy as well when Henry invaded Normandy and defeated him. Robert ended his days in captivity.

The situation of the Norman and Plantagenet kings of England being both vassals of the French kings and while also sovereigns remained a bone of contention for a long time afterwards and relations between the Normans/Plantagenets and Capetians/Valois were tense at best. Philippe's son and successor, Louis VI, spent much of his reign at odds with Henry I of England (the aforementioned Henry Beauclerc). Louis frequently sheltered Henry's rebellious nephew, William Clito (only son of Robert Curthose), because he was a useful ally against Henry and the Normans.

Sources:

Bartlett, Roger. (2000). England Under the Norman and Angevin Kings 1075–1225. ‎Oxford University Press.

Bradbury, Jim. (2007). The Capetians: The History of a Dynasty. Bloomsbury Publishing.

Cantor, Norman. (2015). The Civilization of the Middle Ages: Completely Revised and Expanded Edition. Harper Paperbacks.