Labgenetics is one such company. Set up in a Madrid suburb in 2003, it does almost 30 percent of its business with French customers.
"In France, the law bans a father from seeking a paternity test without a judge's authorization," said the firm's technical director, Jorge Puente.
Labgenetics offers "paternity kits" over the Internet to men who want to confirm they are the biological fathers of their child.
Sent in a plain envelope, the kit consists of an information sheet and a set of tubes containing cotton buds, one for the "presumed father" and the other for the child.
The "father" is asked to rub the cotton bud on the inside of his cheek to pick up cells from the mouth, and to do the same for the son or daughter.
The DNA from the two samples are then compared.
The company promises a response, by letter or fax, within three days, for a fee of 395 euros (587 dollars).
It says that, in the case of a positive result, the test is "more than 99.9999 percent" accurate.
The procedure, often sought following a separation, is restricted by law in France.
"The identification of a person by their genetic fingerprint ... outside of a judicial procedure" is punishable by a year in prison and a 15,000-euro fine, according to French law.
But many French fathers seem willing to take the risk. A growing number use the Internet to contact companies in other countries which allow it, such as in Spain.
In the southern city of Seville, the Spanish headquarters of DNA Solutions -- a sort of multinational for the genetics industry with offices in about 30 countries -- proudly announces that "80 percent of our customers are French."
The company, based in Australia, currently has a special promotion on paternity kits for 199 euros.
But "the results are private and informative and have no legal value in France," warned Elena Iglesias, administration director of DNA Solutions Spain.
Paternity tests are the main activity of about 10 private companies based in Spain which specialise in DNA.
"It's a profitable business, but one which is very price competitive," said Puente, of Labgenetics.
In addition, these small and medium-sized companies are increasingly trying to diversify.
DNA Solutions offers a whole range of DNA-linked services, in particular a test, on the English version of its website, that can tell you the geographic origins of your ancestors for 139 pounds (around 200 euros).
At Labgenetics, Puente is sceptical about the commercial viability of this type of service and prefers to diversify into private detective work.
The firm recently was able to determine who among about 50 employees of a certain company was habitually relieving themselves on the toilet floor.