On the mark TA
I did same variations to Paris, Tel Aviv, Pragh. Sometimes with miles sometimes paid for LH ticket. The fares FRA to CDG are dirty cheap if you stay over Saturday-Sunday night. It payed to buy a ticket and accrue the miles. Elsewhere I bought award tickets with UA miles (on C). If one wants to go F then one may buy the ticket and U/G with UA miles. As I recall the fares FRA to ATH were expensive so may be miles are good deal. Those are seasonal decisions and icorporate an over Saturday-Sunday night stay for best fare results.