In this study, a class of weighted, monotone and structure-preserving Du Fort-Frankel schemes are constructed for solving one-dimensional (1D) and two-dimensional (2D) nonlinear Allen-Cahn equations, respectively. As parameters θ, β and grid-ratios satisfy suitable conditions, numerical solutions obtained using the current methods satisfy the discrete energy-dissipation laws, monotone increases, and the discrete maximum bound principles. Furthermore, by using the discrete and continuous maximum bound principles, maximum-norm error estimates have been derived, rigorously. Although the current methods are conditionally consistent, they are very easy to be implemented and cost less than some the existent methods because of their explicitness. Finally, numerical results confirm the exactness of theoretical findings, and simulate interesting physical phenomena.