If we can build plants that are as huge and complex and expensive as fission plants, then about the same effect, but without the fuel / proliferation / waste problems (which is nothing to be sneezed at).
If the cost is low, a brave new world with fusion replacing fossil generation as quickly as they can be built. Energy-inefficient processes like desalination and cracking water for hydrogen become attractive.
If the cost is very high, it may be that renewables have stolen fusion's market slot. In that case we'll see some national prestige projects, but against a broader renewable energy market.
I'm not sure that it would have a profound effect at all. Fission is very power dense as well and fission fuel cost is not the primary driver of overall costs in existing nuclear designs.
Fusion might end up looking a lot like fission, but hopefully with a lower perceived safety risk and thus more public acceptance.
Granted, modern fission designs aren't actually unsafe, but that doesn't matter for PR purposes.
I hear sometimes contradictory hear-say on the lines of "unlimited energy", "reactor would have to be fed constantly".