In this paper, we define new classes of circulant matrices, namely, n-parametric and bigeometric circulant matrices. The lower and upper bounds for the spectral norms of particular cases of these matrices are given. Moreover, the spectral decomposition of the n-parametric circulant matrix structure is determined using a Vandermonde matrix, which allows the set of n-parametric circulant matrices to be defined as a noncommutative ring with unity. An expression for the determinants of these matrices is presented. Additionally, we introduce the definition of a bi-geometric circulant matrix, present a closed expression for its Frobenius norm, and provide an upper bound for its spectral norm. Moreover, explicit expressions for the eigenvalues of an n-parametric circulant matrix, whose entries are the Horadam, Fibonacci, Lucas, Jacobsthal, and Pell numbers, are presented.