While both answers answer the specific case, would like to explain a bit more broadly, since the question is a lot more broadly worded than the specific instance. Since the player has hexproof, but the card Draconic Roar does not say 'target player', all effects of the spell will occur. However, a very similar card, Searing Blaze instead reads:
Searing Blaze deals 1 damage to target player and 1 damage to target creature that player controls.
In this instance, if your opponent had Leyline of Sanctity out, you would not be able to cast Searing Blaze targeting your opponent's creature, because in order to cast a card, you have to have a valid target for each instance of target of the card, and you can't target your opponent. If you have a creature though, you could still cast it targeting yourself and your creature.
Now, a bit more niche of an instance that still is relevant to the general question at hand: lets say your opponent has Leyline of Anticipation out, as well as a creature. You cast Searing Blaze targeting them and their creature. In response, they cast Leyline of Sanctity, giving themselves hexproof when it resolves. Searing Blaze will still resolve and deal 1 damage to their creature (or 3, if Landfall is in effect), but won't deal any damage to them.