King Philip of France is a worthy opponent for King John—but that doesn't mean that he's an especially interesting or attractive figure. Mainly, he seems a good match for King John in his negative qualities: both men are shifty, self-interested, and prone to picking fights, and both suffer from short attention spans.
You can see King Philip's belligerence in the opening scene of the play, when he sends a provocative message to King John (through his messenger, Châtillon), basically telling King John that he isn't a real king and that he should therefore give up his claim to the crown... and also surrender various territories to his nephew Arthur.
Do we think there is any chance that King John would agree to these terms? No. Do we think King Philip thinks there is any chance that John will agree to them? Not likely. So, you could pretty easily say that, in sending this message, King John is basically asking for war.
In theory, he's picking the fight on behalf of young Arthur, King John's nephew, who does indeed have a good legal claim to the throne of England. But from the way Philip carries himself in negotiating on Arthur's behalf, it starts to look like Philip is really only interested in using Arthur as a pawn so that he himself can take control of King John's territories.
The proof that Philip doesn't really care about Arthur comes when Hubert suggests that Philip's son Louis marry John's niece Blanche. Now that he has an opportunity to secure a good deal for his own son, Philip couldn't care less about young Arthur. All of a sudden, he and John are the best of friends—because it serves both of their selfish interests.
That said, if there's one lesson that King John teaches us about politics, it's this: somebody who betrays one friend for the sake of personal gain will betray any friend who stands in his way. Just as King Philip kicked Arthur to the curb when it no longer suited him to back him up, Philip will also abandon John once Pandolf (representing the Pope) commands him to do it.
Sure, Philip puts on a public show of not wanting to break his alliance with John—but do we really believe he's sincere? If he really valued his friendship with John, couldn't he tell Pandolf to take a hike just like John does?
Philip's behavior proves that, as the Bastard would put it, "commodity" controls his actions.
This the last major decision Philip takes in the play. Like his English counterpart John, Philip seems to wither in power and importance in the second half of the play. Just as John gives authority for defending England to the Bastard, Philip turns the command of the invasion entirely over to his son Louis. From Act IV onward, Louis is the main commander of the French, not Philip.
It just goes to show that no matter how hard these guys fight and scheme to get power, they're eventually going to lose it and just disappear. That's just how the world rolls. Kind of makes the whole mad dash for power and status seem kind of useless, right?