Assuming df1 is your first dataframe and df2 is your second one, you can merge on the country and perform a left join, you need to rename the country column on df2 first though:
df2.rename(columns={'Country':'Country_Name'}, inplace=True)
merged = df1.merge(df2, on='Country_Name', how='left')
# you can either use merged dataframe or assign it to df1:
df1 = merged
or you can assign it back to df1 instead of to merged:
df1 = df1.merge(df2, on='Country_Name', how='left')
Should give you what you want