Combine the vinegar, sugar, chile, ginger, garlic, and 1/4 tsp. salt in a 2-quart saucepan. Bring to a boil over medium-high heat, stirring occasionally, until the sugar is dissolved, 3 to 4 minutes. Stir in the apricots and mango. Reduce the heat to low and simmer, stirring occasionally, until the fruit is soft and the mixture is thickened, about 25 minutes. Season to taste with salt and let cool to room temperature.
Meanwhile, in a 12-inch nonstick skillet, heat 1 Tbs. of the oil over medium-high heat. Add the sausages and cook, turning occasionally, until well browned, 4 to 5 minutes. Transfer to a cutting board and slice each in half on the diagonal.
Heat the remaining 1 Tbs. oil in the skillet over medium-high heat. Add the fennel, coriander, and cumin seeds and cook, stirring occasionally, until fragrant, about 1 minute. Add the onion and cook, stirring, until just softened, 2 to 3 minutes. Add the cabbage, 1 tsp. salt, 1/2 tsp. pepper, and 1 Tbs. water and reduce the heat to medium. Return the sausages to the skillet, burying them in the cabbage mixture. Cover the pan and cook for about 3 minutes. Uncover and continue to cook until the cabbage is just barely tender and the sausages are hot. Season to taste with salt.
Serve the chutney with the sausages and cabbage.