There are a lot of different roulette bets that you can make, but all of them except one offer the same house edge. I'm included below a list of the English names for each bet, the French name for each bet, and the payoff for each bet.
This bet pays off 1 for 1, and it's just a bet that the ball will land in either a red or black pocket. The French name for a bet on red is "rouge" and for a bet on black it's "noir".
This bet also pays off at even odds. You're betting either that the number will be an even number or an odd number. The 0 and the 00 is neither odd nor even. The French name for a bet on odd is "impair", and the French name for a bet on even is "pair".
A high bet is a bet that the ball will land on numbers 17-36, and a low bet is a bet that the ball will land on numbers 1-18. These bets are also called first eighteen and last eighteen bets. Betting on high or low offers even odds as payouts. The French name for a high bet is "passe" and for a low bet is "manque".
You can bet on sets of 12 numbers at a time, and if you win, this bet pays off at 2 to 1. You can bet on 1-12, 13-24, and 25-36. In French, these are called "premier douzaine" for the first dozen, "mayenee douzaine" for the middle dozen, and "`derniere douzaine" for the last dozen.
A bet on a single number pays off at 35 to 1. In French this is called "en plein".
A "split" bet is a bet on two numbers, and it pays off at 17 to 1. The bet is made by placing it on the line between two numbers. In French this is called "a cheval".
A "street bet is a bet placed on 3 numbers, and it pays off at 11 to 1. To place this bet, you put your chips on the line at the left of a row of three numbers. In French this bet is called "transversale".
A "corner" bet is placed on 4 numbers. It pays off at 8 to 1. To make this bet, you play your chips at the intersection of the 4 numbers you want to bet on. In French this bet is called "carre".
On a single zero roulette wheel, there is another bet you can make on the first four numbers, 0, 1, 2, and 3. This has the same payoff but a different French name, "quatre premiere".
This bet only exists on an American roulette wheel, and it's a bet on the 0, the 00, and 1, 2, and 3. This bet has a higher house edge (7.89% compared to 5.26%) and only pays off at 6 to 1.
If a street bet is a bet placed on 3 numbers, you might assume that a "double street" bet is placed on 6 numbers. You'd be right, too. You place this bet at the intersection of the two lines at the end of 2 rows of 3 numbers. The French name for this bet is "sixaine". This bet pays off at 5 to 1.