Orthogonal Frequency Division Multiplexing (OFDM) is the dominant waveform in modern wireless systems, but suffers performance degradation in high-mobility environments due to Doppler-induced inter-carrier interference and unreliable pilot-based channel estimation. Neural receivers have recently shown strong performance in OFDM systems by learning equalization and detection directly from the received time-frequency grid. However, when channel estimation becomes unreliable, receiver-side learning alone is insufficient to fully recover performance. In this work we introduce DeepOFDM, a learnable modulation framework that augments conventional OFDM with a lightweight convolutional neural network (CNN) modulator jointly optimized with a neural receiver. Instead of mapping symbols independently to resource elements, DeepOFDM spreads information across local time-frequency neighborhoods while remaining fully compatible with FFT-based OFDM processing. The learned modulation breaks the rotational symmetry of conventional QAM constellations, enabling the receiver to infer residual phase directly from data symbols. This structure allows reliable operation with sparse pilots and even in fully pilotless settings. Extensive simulations demonstrate improvements in block error rate and goodput under high Doppler, while over-the-air experiments confirm practical feasibility. These results highlight the potential of transmitter-receiver co-design for robust and spectrally efficient AI-native physical layer design.