Please be careful not to suggest old time-tables.... You will get to Kyoto Station within about 4 and a half hours of Narita International Airport.
Narita Express [N'EX] trains which depart before 12:00 noon all stop at Shinagawa Station.
It is far easier to make a transfer at Shinagawa, from N'EX to Shinkansen, than at Tokyo.
To take a N'EX train of JR-East, you need to reserve your seat.
I recommend your trying reserving also your Shinkansen seat;
Shinagawa is the second station for westbound Shinkansen after greater station Tokyo, where non-reservation cars can become crowded.
Narita International Airport [NRT]
: Terminal 1 : Narita Airport Station.
: Terminal 2 : Airport Terminal 2 Station.
Two railroad operators each have stations of these names.
If your flight is Air France # 272, then your terminal is Terminal 1.
http://www.narita-airport.jp/en/guide/step/index_t1.html
After immigration procedures at NRT, go to the basement floor, and find JR-East Travel Service Center. When it's not open, then find Ticket Office around it.
JR-East station attendants also handle tickets for Shinkansen of other JR companies.
http://www.jreast.co.jp/e/travel_info/service_center/index.html
You can ignore a Suica & N'EX package (which includes a discount ticket) if you don't mind paying 1,410 yen more. In that case, your payment will be within 16,630 yen.
Your N'EX train arrives at Shinagawa Station into Track 14 or 15, near Shinkansen tracks.
Then go up to the concourse floor and find a Shinkansen North / South Transfer Gate.
Your Shinkansen train departs from Track 23 or 24 at Shinagawa Station,
and arrives into a track on the south side of Kyoto Station.
Departures from airport -- Shinagawa Sta. -- Kyoto Sta.;
07:44 / 07:46 N'EX 2 -- 09:40 Hikari 507 -- 12:15 ;
07:44 / 07:46 N'EX 2 -- 09:27 Nozomi 217 -- 11:41 ;
08:13 / 08:16 N'EX 4 -- 10:10 Hikari 467 -- 12:48 ;
08:13 / 08:16 N'EX 4 -- 09:54 Nozomi 221 -- 12:08 ;
08:50 / 08:53 N'EX 6 -- 10:40 Hikari 509 -- 13:15 ;
08:50 / 08:53 N'EX 6 -- 10:27 Nozomi 225 -- 12:41 ;
09:15 / 09:18 N'EX 8 -- 11:10 Hikari 469 -- 13:48 ;
09:15 / 09:18 N'EX 8 -- 10:57 Nozomi 109 -- 13:11 .
Consult a station attendant in your NRT terminal on whether you can catch an earlier Shinkansen train.
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