First, the full name of your town Le Becquet was Saint-Crespin-du-Becquet. In 1815, it merged into the town of Belbeuf, by which it is now known.
All of the birth, marriage, and death records for the département of Seine-Maritime, where Belbeuf is located, were recently put online by the departmental archives, and are free for you to access. Belbeuf is a small place so your research will not be difficult.
The records before 1793 are church parish registers (« registres paroissiaux »), and from 1793 forward are civil records (« état civil »).
The civil records after 1793 are indexed. There are 10-year indexes (« tables décennales ») for each town (« commune ») by decade beginning with "3", e.g. 1793-1802, 1803-1812, 1813-1822, etc. with separate indexes for births (« naissances »), weddings (« mariages »), and deaths (« décès »). --- To find your ancestors, you will start by looking at the « tables décennales » for Belbeuf for 1843-1852 and 1853-1862.
You will also find annual indexes after 1793 for every year in every register.
Here is the link to the Archives départementales de la Seine-Maritime:http://www.archivesdepartementales76.net/
The best place to do collaborative French research and see what other genealogists may have found about one of your family lines is GeneaNet.org . GeneaNet is the largest site for French genealogical research in the world, with user contributed data on more than 960 million people (!). You can register and do limited types of basic searches for free. However, I highly recommend that you join the Club Privilège - only 40 euros per year - which gives you access to powerful tools to do searches by individual with multiple criteria (dates, places, spouses, etc.), and access to numerous other resources, including some collections of digitized records.
I hope this gives you a good start.
Bonne quête !