Immigration/Customs question (first-time international traveler)

You go through immigration/border control when you enter the Schengen Zone, which in this case is Frankfurt.

This article may, or may not, allay your concerns.

http://www.independent.co.uk/travel/can-i-really-transfer-between-flights-in-just-50-minutes-a6754241.html

"..... there isn't much room for error." There is no room for error. Your flight from Houston could very well be late, then what? The company travel agency has done you a great disservice and should be made to change the booking. You will have to go through Passport Control at Frankfurt certainly and then find your way to the gate for Valencia and even if your plane lands on time and you deplane IMMEDIATELY (unlikely) 50 minutes is not enough time. My guess is that the T.A. has never had to go through immigration in a European airport. Insist on a proper booking, especially for your first international travel experience.

That does sound like a short time for the connection but the booths and the officials at Frankfurt airport are efficient -- I think you'll need to wait in line briefly to get your passport stamped but it goes quickly, so as long as the gate for the flight to Valencia isn't too far away, you'll be ok. (This assuming any checked baggage is checked all the way through on one ticket, and that you're traveling on one complete ticket) Don't let the look/feel of the airport lighting and furniture get you too worried; the rest of Europe isn't so cold and uninviting. Ditto the food -- you'll be pleasantly relieved that Valencia is nothing like Frankfurt.

I would not be concerned. If you miss your plane they have to rebook you on the next one. In May we are flying to Europe via Iceland by Iceland Air and have only 30 minutes to change the planes and go through a passport control but that's the way Iceland Air booked it. They should know so I am not stressing about it.

Is this one ticket or two? Is this a through booking?
Assuming this is a through booking:
You will go through immigration for entering the Schengen Area when you land in Frankfurt. Depending on your nationality your passport may or may not be stamped (you don't say your nationality).
Frankfurt to Valencia is an intra-Schengen intra-EU flight, no immigration (but the airline may check your passport as ID).
At Valencia you will collect your luggage and go through customs. The label on your luggage will show it came from outside the EU and so is liable for customs check. But, don't worry, just walk through the green "nothing to declare" door, 99% of passengers are not stopped.

50 minutes is tight, you have to hope there are no delays on your first flight. But, if it is a through booking and you miss your connection because the first flight is late, that is the airlines responsibility to put you on the next flight.

They have to book you on the next AVAILABLE flight. And only if the flights are on the same ticket.

The next available flight might not be that day or in extreme cases not even that week. If this was booked as two separate tickets then if you are late for your connection you are a no show and they don't have to do anything for you.

It is booked as one ticket. We are flying with United/Lufthansa. Our itinerary shows us both arriving and flying out of terminal 1, so I'm hoping the gates are close, as it will be with the same airline. However, I have read that Frankfurt is a very LARGE airport. I am a US citizen, so I don't know if that will help any with immigration. Are the immigration stations close to the gates, or will we have to walk a fair distance?

You say "I am a US citizen ...". Actually, if you were travelling on an EU passport, not a US passport, it would be a quicker trip through Immigration.

I am a US citizen, so I don't know if that will help any with immigration.

No, that will make it worse. There are two sections "EU" and "Non-EU". EU is fast, as they just check the passport/ID-card is good. Non-EU (and that includes the US), they have to check you are legal, have not exceeded your 90 days, stamp the passport. All of which takes time. Frankfurt is efficient, I would guess 5-20 minutes for non-EU immigration.
that doesn't leave much spare is your flight is late.

This reminds me of a New Yorker magazine cartoon from many years ago. A confused looking lady is in line at passport control at a foreign airport. An airport employee tells her she is in the wrong line and needs to go the "Foreign Passport" queue. She says "But I'm not a foreigner, I'm an American."

It can take a long time - 15-20 minutes - just to get off the plane.

I wasn't trying to imply that my being from the US was somehow better (or worse), just trying to add clarification so I can get accurate information. A previous poster stated that I didn't list my nationality. Sounds like it's going to be close...great.

One of thing you need to push for are seats near the exit so that you can get off quickly and run. We have a 90 minute connection in Amsterdam that we missed because we didn't pay attention to our seats and were in the far corner of the plane. It took 20 mins or a better more to get off and then of course the immigration line. Fortunately they had lines for people with short connections. Unfortunately we didn't notice that until we had been in line for another 20 minutes or so. So look around as they might have short connection lines. We missed our connection by about two minutes. That was more than the extra time it took to get off and the not seeing the short immigration line. Good luck - you may need it.

To add to what Frank said, it's very important to try and get seats either in Business Class or at the front of the plane so that you can deplane as quickly as possible. You'll need to get to Passport control before the rest of the passengers from your flight, so that you don't have to wait in a long queue. Keep in mind that there could be other flights arriving at the same time and they will be waiting in the queue as well. You will likely have to go through security again before boarding your ongoing flight to Valencia, and that will take time as well.

It will also help to not have heavy or cumbersome carry-on luggage, as you'll need to move quickly. I've had a 60 minute transfer in Frankfurt in the past, so my comments on based on experience. Don't stop for coffee on the way to your next gate!

I should add that I've found Frankfurt to usually be very fast and efficient in processing passengers, especially if they know you have limited time to make a flight connection. As you're traveling on what appears to be a code share flight, it will be in the airline's interest to make sure you make the connection, as it will be their responsibility to get you to the end destination.

Frankfurt has been a major international gateway for many decades. Like all such airports it maintains an extensive website. Instead of "hoping" about your arrival and departure points, look them up:
https://www.frankfurt-airport.com/en/flights---more/transfer.html
Terminal maps are helpful navigational tools. I print them out; others smart enough to have a smart phone or other such device can download.
Also copy the Lufthansa schedule to Valencia for the day so if you miss your scheduled plane you can negotiate with Lufthansa about a later connection.
Others have pointed out that the 50-minute clock starts running at touchdown, not when you are off the plane. At the other end of that time span, you cannot arrive at the departure lounge one minute before the stated time of departure and expect the airplane door to still be open. You will need to hustle to make this transfer. And don't be afraid to ask Lufthansa ground staff for help.

Honestly, don't get too stressed about it in advance. People are making this sound impossible. I've made many short connections. Just follow the signs and walk quickly through the airport; don't stop to use the restroom or buy a water. In the worst case, the airline will get you on a later flight. If your flight is significantly delayed and it looks like you will miss your connection, ask one of the flight attendants for advice. They may be able to check the status of your next flight or direct you to an airline desk where you can get assistance.

RE: Others have pointed out that the 50-minute clock starts running at touchdown, not when you are off the plane.

See: http://www.bottonline.co.uk/flight-delay-compensation/claim-guides/definition-of-arrival-time

the Court ruled that ‘arrival delay’ corresponds to the time at which
at least one of the doors of the aircraft is opened, the assumption
being that, at that moment, the passengers are permitted to leave the
aircraft. Coby Benson, Flight Delay Compensation Solicitor

And in looking at historic data: https://helpdesk.flightstats.com/hc/en-us/articles/217613088-Is-the-arrival-time-runway-time-or-gate-time-What-s-the-difference-

The arrival gate time includes the time it takes to taxi to the gate.

Of course if you are in the cheap seats and have bulky carry-ons it could take 10s of minutes to get out of aircraft.