Sensors using nitrogen-vacancy centers in diamond are a promising tool for small-volume nuclear magnetic resonance (NMR) spectroscopy, but the limited sensitivity remains a challenge. Here we show nearly two orders of magnitude improvement in concentration sensitivity over previous nitrogen-vacancy and picoliter NMR studies. We demonstrate NMR spectroscopy of picoliter-volume solutions using a nanostructured diamond chip with dense, high-aspect-ratio nanogratings, enhancing the surface area by 15 times. The nanograting sidewalls are doped with nitrogen-vacancies located a few nanometers from the diamond surface to detect the NMR spectrum of roughly 1 pl of fluid lying within adjacent nanograting grooves. We perform ¹H and ¹⁹F nuclear magnetic resonance spectroscopy at room temperature in magnetic fields below 50 mT. Using a solution of CsF in glycerol, we determine that 4 ± 2 × 10^{12 19}F spins in a 1 pl volume can be detected with a signal-to-noise ratio of 3 in 1 s of integration.