Clustering 2D curves
Yes, you could start with k-means on the 100-dim data. Make sure you have normalized your data to perhaps zero mean and unit variance before running k-means.
Use the elbow method (google it) to determine the optimal number of clusters for your data.
By the way you also want to check if the two dimensions are correlated in any way. If it is then you can use PCA to convert the 2 dimensions into a single dimension that explains most of the variance in your data and then cluster using 50-dim per observation.