Neuromorphic computing architectures demand the development of analog, non-volatile memory components operating at femto-Joule/bit operation energy. Electronic components working in this energy range require devices operating at ultrafast timescales. Among different non-volatile, analog memories, ferroelectric tunnel junctions (FTJs) have emerged as an important contender due to their voltage-driven operation leading to extreme energy-efficiency. Here, we report a study on the switching timescale and linear conductance modulation of organic FTJs comprising a metal/ferroelectric/semiconductor (MFS) stack with different morphologies of ferroelectric copolymer P(VDF-TrFE) ultrathin films. The results show that due to different annealing temperatures and protocols, the spin-coated copolymer films are modified significantly, which can have a large effect on the switching timescales and threshold fields of the FTJs with the best quality devices having a projected switching timescale of sub-nanosecond range. An improvement in switching speed by 7 orders of magnitude can be obtained with an increase of the programming voltage by less than a factor of 2 in these devices. This ultrafast switching of ferroelectric domains in our FTJs leads to pico to femto joule range of operation energy per bit opening the pathways for energy efficient and fast operating non-volatile memories while devices with higher domain pinning sites show a route for tuning analog conductivity for bio-realistic neuromorphic architectures.