Michel Sapin said it was clear that Britain had been caught by surprise by the vote to leave the European Union.
"It has been a few months since the referendum took place. You might have thought that certain people had prepared for this," he told reporters.
"No-one was prepared. You can see very well that they are improvising, with flip-flopping between accommodating positions... and harder positions, even a 'hard' Brexit."
Sapin said he believed that the apparent lack of a plan to see through Brexit showed that some members of the government "did not want (Brexit) and that it has created debates within the government which are clearly very difficult".
May said in the speech that she favoured a clean break from the EU and not a "half-in, half-out" deal with Brussels.
Tuesday's speech saw May announce her desire for a so-called "hard" Brexit -- a full break from the EU which entails leaving the single market in order to have full control over immigration.
She said the UK "cannot possibly" remain in the European single market, because if it did remain it would mean "not leaving the EU at all".
May came under fire from worried British expats living abroad, who had been hoping she would offer more of a guarantee of their status.
Brian Cave from France criticised May for not using the speech to guarantee the rights of EU citizens living in the UK which would ensure the status of British citizens living in the EU.
"I do not feel that she really grasps the fear and worry that so many British Citizens in the EU have," said Cave."The impression is that her thoughts were almost completely taken up with the economy and not the effect on ordinary citizens, either at home and certainly not those abroad."
"I would have welcomed it if she had assured British citizens residing in EU states by saying they would continue to have such protection from the UK as they enjoy now, and that their pensions would be protected as the UK remains responsible for their social security."