You may want to try morning glories (though they don't really smell), though they do like watering, or maybe Cardinal climber or snail shell vine.

The hinged casement window opens OUT and you only have about 1 inch clearance from the bottom of the window to the top of the planter. That's a dilemma because you have to open the window to water the box, yes? If not, consider not opening the window more than a crack and then grow whatever you want. Taller plants will lean away from the window eventually.

Even if they do sprawl, vines try to grow up first, so you'd need to work hard to pin them down. Having only about an inch would be tough for vines like Cardinal climber and Carolina Jessamine. I'm thinking if you want something that cascades, it must still stay low. You can sneak a little clearance for a plant by not filling the soil to the top of the box. The type of plant that would work is something like thyme. It would respond well to cutting the tops if you needed to. Not very showy but gets small flowers, stays low, some varieties smell very nice (e.g., lemon variegated), and it cascades:

Ice plant is often available at this time of the year at places like Home Depot (for as little as $10 for a 2 x 2 flat). It cascades as well after about a year if planted right to the edge of the pot, but it's not frost hardy so you'd need to remove the plant before frost in the fall:

You would essentially need to work with these types of low growing plants to not have them impede the window opening. If you wanted to go with low growing annuals you could try even something like alyssum, but I'm not sure if it would cascade.