Field mappings are kind of cumbersome in ArcGIS. First you create a fieldmappings object, then create fieldmap, then add input fields and define output fields. Also, you can add the entire table to the mapping like:
myMapping = arcpy.FieldMappings()
myMapping.addTable(path_to_the_table)
arcpy.Append_management(fc, fc_out, "NO_TEST", myMapping)
I found the following example that I used some time ago when building custom mappings:
in_file1 = 'data.gdb/Trees'
in_file2 = 'Plants.shp'
output_file = 'data.gdb/Vegetation'
# Create the required FieldMap and FieldMappings objects.
fm_type = arcpy.FieldMap()
fm_diam = arcpy.FieldMap()
fms = arcpy.FieldMappings()
# Get the field names of vegetation type and diameter for both original files.
tree_type = "Tree_Type"
plant_type = "Plant_Type"
tree_diam = "Tree_Diameter"
plant_diam = "Diameter"
# Add fields to their corresponding FieldMap objects.
fm_type.addInputField(in_file1, tree_type)
fm_type.addInputField(in_file2, plant_type)
fm_diam.addInputField(in_file1, tree_diam)
fm_diam.addInputField(in_file2, plant_diam)
# Set the output field properties for both FieldMap objects.
type_name = fm_type.outputField
type_name.name = 'Veg_Type'
fm_type.outputField = type_name
diam_name = fm_diam.outputField
diam_name.name = 'Veg_Diam'
fm_diam.outputField = diam_name
# Add the FieldMap objects to the FieldMappings object.
fms.addFieldMap(fm_type)
fms.addFieldMap(fm_diam)
# Merge the two feature classes.
arcpy.Merge_management([in_file1, in_file2], output_file, fms)