The influence of a classical environment on the behaviour of the Wigner function and the concurrence of an accelerated two-qubit system interacting is discussed. The negative values of the Wigner function verify the non-classicality, while the concurrence shows the entanglement degree of the quantum system. We assume one or both observers are accelerated (s) and interact with a common or independent environment. Suppression of the coherence rises due to acceleration effect, noise strength, and noise frequency are pointed. The amount of quantum entanglement is investigated by using the quantum concurrence, where its positive values are consistent with what the negative Wigner function shows. We found that the degradation of coherence of the initial system reduces when observers interact with their environments independently more than when it interacts with a common one. It is also sensitive to the acceleration status of both observers. Additionally, the correlation and entanglement pertinent to the situation with common or independent noise agents behave contrarily for the two regimes of Markovian and non-Markovian noises.