EVs are more expensive initially, but cheaper in the long run. I bought a 20k EUR EV last year (VW e-up, great car). After ~8 years it will be cheaper overall than a 10k EUR ICE car. Petrol prices will probably go up faster than electricity as well, so likely even less.
So apart from subsidizing the purchase price which already happens widely, perhaps the government should provide cheap loans for people who don't have the initial capital to buy an EV.
Also, There are signs we've already hit the peak for conventional oil. This report [1] claims that by the 2030s Europe will see its access to oil reduced by 10-20%. So running an ICE car will only go up from here. There's good reasons to assume the costs of EVs will only go down.
Wrt to the grid, the french grid operator RTE published a study [2] saying that they estimate that by 2035 there will be 15.6 million EVs on the road, a bit half of the 38m total cars on french roads today. The study says this would represent 8-10% of today's electricity consumption and would pose no danger to the stability of the grid. About 2 million new cars are sold here every year, so after 2035 the percentage would go up by 1% every year to 20% or so. A challenge but definitely feasible.
1: https://theshiftproject.org/en/article/oil-what-are-the-risk...
2: https://www-rte--france-com.translate.goog/actualites/develo...