Identify my Motobécane racing bike
I don't know the exact model (probably is Trainer as shown on the top tube decal) but it was likely built sometime right around 1984, most likely 1984-1986 judging by the parts. The brand was known as Motobecane for most of their history. They went bankrupt in 1981 and were bought by the Japanese (Yamaha or Suzuki, I forget which) who relaunched the brand in 1984 as MBK (like many other French bike companies, they made more than just bikes - see also Peugeot). 

The other giveaway is the Sachs-Huret rear derailleur. Sachs and Huret were separate companies - one German, one French - prior to 1980. In 1987 they introduced an indexing system to keep up with SIS which had come out the year prior from Shimano and was a massive hit. In the late 90s the combined company was bought by the American SRAM company. The shift levers look to be friction so that dates them to after the Sachs/Huret merger but before the advent of indexed shifting. 

It is an entry level bike. The big giveaway is the tubing decal which says "Hi Tensile". Hi Tensile (or Hi-Ten) is the lowest grade of tubing used in bikes. Pretty much the same stuff used in Huffy and other department store bikes. That said, not all Hi-Ten is created equal and there are actually some Hi-Ten frames that ride quite nicely even if it's far from being the lightest tubing. Nicer level Motobecanes of the era would have been made using Reynolds 531 or various grades of Vitus steel tubing. 

As you've probably discovered by now the bottom bracket is a regular taper with English threads. Most French bike companies stopped using French threads in the late 70s/early 80s much to the relief of bike shop mechanics everywhere!