Although first developed for the needs of quantum many-body physics and quantum computing, tensor networks (TNs) are increasingly being deployed to solve a wide range of problems in machine learning, optimization, and applied mathematics. Inspired by the distinct implementation challenges of TN methods in these new settings, we present ContracTN, a lightweight Python library for general-purpose TN calculations. Beyond the use of the dense tensor cores supported in standard TN libraries, ContracTN also supports the use of copy tensors, parameter-free objects which allow diverse concepts like batch computation, elementwise multiplication, and summation to be expressed entirely in the language of TN diagrams. The contraction engine of ContracTN also implements a novel form of stabilization, which largely mitigates the issue of numerical overflow arising from the use of low-precision machine learning libraries for TN contraction. Overall, we wish to popularize a collection of methods which have proven invaluable in implementing efficient and robust TN models, in the hope that this can help catalyze the wider adoption of TN methods for problems in machine learning.