Various factors such as ambient lighting conditions, noise, motion blur, etc. affect the quality of captured face images. Poor quality face images often reduce the performance of face analysis and recognition systems. Hence, it is important to enhance the quality of face images collected in such conditions. We present a multi-task face restoration network, called Network Architecture Search for Face Enhancement (NASFE), which can enhance poor quality face images containing a single degradation (i.e. noise or blur) or multiple degradations (noise+blur+low-light). During training, NASFE uses clean face images of a person present in the degraded image to extract the identity information in terms of features for restoring the image. Furthermore, the network is guided by an identity-loss so that the identity in-formation is maintained in the restored image. Additionally, we propose a network architecture search-based fusion network in NASFE which fuses the task-specific features that are extracted using the task-specific encoders. We introduce FFT-op and deveiling operators in the fusion network to efficiently fuse the task-specific features. Comprehensive experiments on synthetic and real images demonstrate that the proposed method outperforms many recent state-of-the-art face restoration and enhancement methods in terms of quantitative and visual performance.