Indeed. Overcapacity for wind and solar is why batteries and other storage solutions are so important since that provides some ability to absorb the excess energy or use it when production dips. Interconnected grids provides similar grid balancing benefits.
A near future thing might be lots of EVs with vehicle to grid capability adding a lot of battery to the grid. Millions of EVs would provide some non trivial amount of capacity. Several manufacturers are starting to supply cars with this capability (e.g. Ford, Kia, and a few others). And of course Tesla is already experimenting with virtual power plants as well.
The future is going to be a messy process of different countries and companies rolling out bits and pieces of infrastructure and technology as it becomes available. It's a fiercely competitive space and it does not favor players that depend on costly solutions that require high energy prices to be economically sustainable. All that will happen in a market with an increasing amount of variety of supply and greater fluctuations in pricing.
This actually has a re-enforcing effect. The more wind, solar, and battery comes online, the less profitable gas plants become. They only generate revenue when they are in use but they still cost money when they aren't producing. Likewise, exporting nuclear energy is not a thing when there is a surplus of cheap renewable energy unless you basically sell the energy at a loss. And turning a nuclear plant off takes a lot of planning. And turning them back on is of course expensive as well.
That's one of the issues France is facing with its domestic nuclear production. It's often cheaper to import wind power from abroad and with a connected grid, power suppliers have the freedom to do so. And of course in areas where prices are higher, home owners are incentivized to find ways to reduce their energy prices by installing solar on their roofs and adding batteries to their house.