The king's gambit

What's the most solid line against the king's gambit?

1.e5 c6

You asked an answerless question. Such a line doesn't exist in an aggressive opening like the King's gambit.

There's at least one free course on Chessable and other paid ones that are more complete. At the highest levels (in long time controls) , the KG is rarely played since it's considered refuted. Nepo is known to play it and has a course for it, but it's dangerous if the opponent knows the theory.

When playing black, I always play :
1. e4 e5
2. f4 d5

When I play white, that response by black is one of those I don't expect.

'Considered refuted.' Well, if the likes of Boris Spassky have used it at top level, I would say that 'considered old-fashioned' might be more accurate. From an admittedly very brief look on the internet, a 'Modern' defence is "pleasant" for black. I use KG all the time as white and find that there are different ways of dealing with various defences, even if they do take me out of conventional king-hunting a lot of the time.

Consider the Falkbeer Countergambit. It's solid and allows you to get significant amounts of play against the white position.

If I remember correctly, GM Kaufman suggested 1 e4 e5 2 f4 d5 3 exd5 exf4 4 Nf3 Nf6.

@coledavis , to be fair, it's been a while since Boris played at the top level. Also, I don't have Chessbase here at work but I'd suspect he didn't play it in his WC matches... I welcome being wrong on that.

I recommend you follow the line given above by @kindaspongey.