How do I get an ENUM constant for the integer value?

You should assign an integer every month, then just convert.

public enum Mes
{
    Janeiro = 1,

    Fevereiro = 2,

    Marco = 3,

    Dezembro = 12
}

Mes mes = (Mes)12; //mes = Mes.Dezembro

Console.WriteLine(mes); //Dezembro

See working at DotNetFiddle

Another way is to use a method that is responsible for taking a description of the enum. For example in the month of March, it was written as "milestone" to return the written name correctly add this method to your project:

/// <summary>
/// Método responsável por mostrar o user friendly names dos enums, apenas adicionando [Description("Nome Amigável")] e utilizar enum.GetDescription()
/// </summary>
/// <param name="value">enum</param>
/// <returns>String com o nome do enum</returns>
public static string GetDescription(this Enum value)
{
    Type type = value.GetType();
    string name = Enum.GetName(type, value);
    if (name != null)
    {
       FieldInfo field = type.GetField(name);
       if (field != null)
       {
           DescriptionAttribute attr = Attribute.GetCustomAttribute(field, typeof(DescriptionAttribute)) as DescriptionAttribute;
           if (attr != null)
           {
               return attr.Description;
           }
       }
    }
    return null;
}

And decorate your enum like this:

public enum Mes
{
    [Description("Janeiro")]
    Janeiro = 1,

    [Description("Fevereiro")]
    Fevereiro = 2,

    [Description("Março")]
    Marco = 3,

    [Description("Dezembro")]
    Dezembro = 12
}

Make the call this way:

Mes mes = (mes)3; //mes = Mes.Marco

ConsoleWriteLine(mes.GetDescription()); //Março

I hope you can help.

I think the intended one will be something of a style:

Mes mesEnum = "Janeiro".ToEnum<Mes>();

This situation can be checked in other discussions.

I found an example in English, but you can check what you find in Portuguese if you look good.

link