The suggestions to ask for the lowest row are a great idea - you can enjoy everything but still know that you are really not very far off the floor.
Something that might help is that once the rows are raised up into place, you are basically stationary. There are a few minimal effects to make it feel like you are flying, but (to me) they are not scary- no sensation of "tipping over", "dropping", etc that would make you feel like you were about to fall. However, the video on the screen gives the illusion that you are hang gliding over a variety of locations in California - ocean, mountains, etc, so what you are seeing feels like you are are up in the air....don't know if that would bother you. The screen doesn't go all the way around the sides, so if you need to, you can look to the side and see the edges for a "little less illusion". My husband does not like heights and held on tight the first time or two that we rode it. Now he is comfortable that we really aren't very high, and he loves it. (By the way, the lights are very dim when you "lift off" but it's just a few seconds and then the film starts - same at the end when you come back down.)
About 5 sec in, this video shows guests being seated in the front row (which goes the highest).
Here is a video of the ride to see if it will make you feel like it's too high for you to be comfortable, it also gives you an idea of what the ride vehicle looks like.
This is a picture taken from the vantage point of the middle row once the 3 rows are lifted into place. It's from Wikipedia, the info there gives a good overview of the ride and it's effects.
http://en.wikipedia.org/wiki/Soarin'_Over_California
[sorry for tmi]