Not an R expert, but that page you linked to has an atrocious explanation. Two variables, lambda1 and lambda2, and for each the only explanation is lambda? Generally speaking, the elastic net needs two major parameters, which are a regularization factor (in python it is called alpha) and a ratio of L1/L2 penalties (determines the mixture of lasso and ridge regressions).

I will point you to the original implementation by Hastie (who I think first described it):

https://cran.r-project.org/web/packages/elasticnet/

There is a little tutorial here. If you are open to python, I suggest you try here.