How to Sous Vide Filet Mignon to Medium Rare
130F (approx. 54C) works great. That brings it to the very bottom of the "medium-rare scale", allowing you to sear before presentation without overcooking.

Although, I have to tell you, filet mignon is kind of a waste with sous vide. Not that it won't be great, but a much less expensive cut can be cooked at that temperature much longer and give you amazingly tender results.

The minimum time for a medium-rare filet would be just as long as it takes for the whole steak to reach 130F (half an hour or 45 minutes, depending on the thickness of the steak). Of course you can cook it longer, that's one of the beauties of sous vide, but that won't make it any better.

You can spend a whole bunch less money and get chuck (shoulder) and slice it into steaks. Sous vide it for two days at 130F, and that makes a steak almost as tender as filet, yet more flavorful.



That is my very first chuck steak cooked at 131F for two days, then seared. I used a NASA hot cast-iron pan for the searing, so 1°F less will give you a little bit more time to sear without risking overcooking your filet (which would be really tragic!). 

Key Point: As Jefromi says in his answer, medium-rare is a scale. If you do 130F this time, consider carefully as you eat. Is the temperature absolutely perfect for you? Keep track of the temperatures you use every time you sous vide and your impressions at that temperature. Once you know what temperatures are perfect for you, sous vide allows you to duplicate perfection perfectly.