I don't know exactly how it is that you had chosen to go about integrating the two frameworks but from experience I can tell you that it works.
for example my struts-config.xml has the following:
<struts-config>
    <!-- ================== Form Beans ================ -->
    <form-beans>
        <form-bean name="UploadForm" type="com.foo.bar.forms.UploadForm" />
    </form-beans>
    <!-- ================== Action Mapping Definitions ================ -->
    <action-mappings>
        <action path="/pages/UploadFiles" name="UploadForm"
            type="org.springframework.web.struts.DelegatingActionProxy" scope="request"
            input="/pages/ImportFiles.jsp">
            <forward name="success" path="/pages/SwitchView.do" />
        </action>
    <!-- ================================ Plugins ============================== -->
    <plug-in className="org.springframework.web.struts.ContextLoaderPlugIn">
        <set-property property="contextConfigLocation"
            value="/WEB-INF/action-servlet.xml, /WEB-INF/applicationContext.xml" />
    </plug-in>
</struts-config>
my action-servlet.xml file contains the following bean definition:
<bean name="/pages/UploadFiles" class="com.foo.bar.actions.UploadFilesAction" />
This way Struts-1 retains control of the MVC but Spring "manages" the whole application.
Hope it helps
EDIT:
your web.xml should alos have the following:
<listener>
    <listener-class>org.springframework.web.context.request.RequestContextListener</listener-class>
</listener>
<servlet>
    <servlet-name>context</servlet-name>
    <servlet-class>org.springframework.web.context.ContextLoaderServlet</servlet-class>
    <load-on-startup>1</load-on-startup>
</servlet>
EDIT 2:
  Hmm, in your struts-config, you set
  the type for your form
  (com.foo.bar.forms.UploadForm) like
  me.
  
  My code work but it's strange struts
  manage form beans and spring manage
  other beans.
I don't think it is strange at all...
  Concretely, I would like to know if
  it's possible to do that
Yes
add the bean:
<bean name="CaseUpdateForm" class="com.foo.bar.forms.CaseUpdateForm" >
and convert the bean above to:
<bean name="/pages/UploadFiles" class="com.foo.bar.actions.UploadFilesAction">
   <property name="updateForm" ref="UpdateForm" />
</bean>