Chess Opening Theory/1. e4/1...e6/2. Nf3/2...d5/3. e5/3...c5/4. b4

White gambits the b-pawn in order to steer Black's c-pawn away from the centre. There isn't much theory in this line due to it being relatively rare. Despite being an unorthodox opening, it is a fairly sound way to meet the French defence.^[1]

4...cxb4, accepting the gambit, is the most principled move. White is usually quick to offer the a-pawn as well, but this sacrifice is less likely to be accepted by Black.

Black can also choose not to accept the pawn, and they might not even be worse off in doing so.

4...b6 tries to stabilise the centre and trade light-squared bishops. After 5. c3 Black has to respond with 5...Qd7 to not lose the bishop after ...Ba6.

4...d4 grabs space in the centre and tries to slow down White's development.^[2]

1. e4 e6 2. Nf3 d5 3. e5 c5 4. b4

Wikipedia has related information at French Defence.